A compact, dense object with a mass of 4.10 kg is attached to a spring and is able to oscillate horizontally with negligible friction. The object is pulled to a distance of 0.200 m from its equilibrium position, held in place with a force of 29.0 N, and then released from rest. It then oscillates in simple harmonic motion. (The object ocillates along the x-axis, where x = 0 is the equilibrium position.) (a) What is the spring constant (in N/m)? N/m (b) What is the frequency of the oscillations (in Hz)? Hz (c) What is the maximum speed of the object (in m/s)? m/s (d) At what position(s) (in m) on the x-axis does the maximum speed occur? (e) What is the maximum acceleration of the object? (Enter the magnitude in m/s2.) m/s? (f) At what position(s) (in m) on the x-axis does the maximum acceleration occur? X = ± (g) What is the total mechanical energy of the oscillating spring-object system (in J)? (h) What is the speed of the object (in m/s) when its position is equal to one-third of the maximum displacement from equilibrium? m/s (i) What is the magnitude of the acceleration of the object (in m/s) when its position is equal to one-third of the maximum displacement from equilibrium? m/s2

A compact, dense object with a mass of 4.10 kg is attached to a spring and is able to oscillate horizontally with negligible friction. The object is pulled to a distance of 0.200 m from its equilibrium position, held in place with a force of 29.0 N, and then released from rest. It then oscillates in simple harmonic motion. (The object ocillates along the x-axis, where x = 0 is the equilibrium position.) (a) What is the spring constant (in N/m)? N/m (b) What is the frequency of the oscillations (in Hz)? Hz (c) What is the maximum speed of the object (in m/s)? m/s (d) At what position(s) (in m) on the x-axis does the maximum speed occur? (e) What is the maximum acceleration of the object? (Enter the magnitude in m/s2.) m/s? (f) At what position(s) (in m) on the x-axis does the maximum acceleration occur? X = ± (g) What is the total mechanical energy of the oscillating spring-object system (in J)? (h) What is the speed of the object (in m/s) when its position is equal to one-third of the maximum displacement from equilibrium? m/s (i) What is the magnitude of the acceleration of the object (in m/s) when its position is equal to one-third of the maximum displacement from equilibrium? m/s2

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter12: Oscillatory Motion

Section: Chapter Questions

Problem 18P

See similar textbooks

Related questions

Q: A 0.80 kg, end mass attached to an ideal spring oscillates horizontally with a period of 0.50s, what…

Q: A 314 g object is attached to a massless spring and executes simple harmonic motion with a period of…

A: a) The total energy of the system is the addition of the spring potential energy and kinetic energy.…

Q: A mass-spring system oscillates on a frictionless horizontal surface in simple harmonic motion with…

A: Amplitude (A) = 0.2 m Let the force constant = k

Q: A mass-spring system oscillates on a frictionless horizontal surface in simple harmonic motion with…

Q: When an object of mass m1 is hung on a vertical spring and set into vertical simple harmonic motion,…

Q: A block–spring system vibrating on a frictionless, horizontal surface with an amplitude of 5.0 cm…

A: At the moment the mass is temporarily at rest, the total energy of the spring-mass system equals the…

Q: Consider a ball of mass mm attached to a spring of stiffness kk, oscillating with amplitude AA on a…

A: Consider a ball of mass mm attached to a spring of stiffness kk, oscillating with amplitude AA on a…

Q: A 2-kg block is suspended from a spring having a stiffness of 800 N/m. If the block is given an…

A: Given: The mass of the object is 2 kg. The spring constant is 800 N/m. The displacement of the…

Q: A 0.1 kg object oscillates as a simple harmonic motion along the x-axis with a frequency f 3.185 Hz.…

Q: kg frictionless block is attached to an ideal spring with force constant 315 N/m. Initially the…

A: We know that the inSHM equation of motion is given as x(t) = A sinωt where A is amplitude ω is…

Q: A 0.550 kg block attached to a light spring oscillates on a frictionless, horizontal table. The…

A: The displacement of the block performing simple harmonic motion is represented as xt=Asin ωtwhere A…

Q: A mass-spring system oscillates on a frictionless horizontal surface in simple harmonic motion with…

Q: Chapter 15, Problem 031 A 9.18 kg object on a horizontal frictionless surface is attached to a…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: 1) A0.1 kg object oscilltes as a simple harmonic motion along the x -axis with a frequency/= 3.185…

A: According to the guidelines issued by the company we are supposed to answer only first question.…

Q: When a 0.20-kg block is suspended from a vertically hanging spring, it stretches the spring from its…

Q: A mass-spring system oscillates on a frictionless horizontal surface in simple harmonic motion with…

A: In a SHM, U = 12kx2 K = 12k(A2-x2) K=3U 12k(A2-x2) =3x 12kx2 x= ±A2 =± 0.1 m

Q: A mass-spring system oscillates on a frictionless horizontal surface in simple harmonic motion with…

A: Using concept of conservation of total energy i.e kinetic energy and potential energy in SHM we…

Q: A simple harmonic oscillator consisting of a 2.5 kg body is attached to the spring with a force…

Q: A 0.28-kg block on a horizontal frictionless surface is attached to an ideal massless spring whose…

A: Given: The mass of the object is 0.28 kg. The spring constant is 500 N/m. The amplitude of the…

Q: A system, consisting of a mass M connected to a spring, oscillates on a frictionless surface with…

A: Ans. (C) neither O, X nor Y

Q: A simple harmonic oscillator consists of a block of mass 2.10 kg attached to a spring of spring…

Q: When a 0.20-kg block is suspended from a vertically hanging spring, it stretches the spring from its…

A: A block attached to horizontal spring is pulled ( on frictionless surface)

Q: 4:30 O M N ll 94% É A block of mass m = 5 Kg is attached to a spring of spring constant k. The block…

Q: What is the error propagation of the period of a pendulum consisting of a 6-kg object oscillating on…

A: The formula for the time period is: Substitute the known values and solve as:

Q: A mass-spring system oscillates on a frictionless horizontal surface in simple harmonic motion with…

A: Given that the value of amplitude and energy of the system is equal to 3 times its elastic potential…

Q: A simple harmonic oscillator consists of a 2.0-kg block and a 1200-N/m spring. When the block is 3.5…

A: The mass of the simple harmonic oscillator is m = 2.0 kg. The spring constant is k = 1200 N/m. The…

Q: The formula for a simple harmonic oscillator is x(t) = Acos (ωt + φ) 1. A block of mass 4.3…

A: The first three questions has been answered. 1. the contact distance is 3.6 m -0.40 m =3.20 m. The…

Q: A mass-spring system oscillates on a frictionless horizontal surface in simple harmonic motion with…

A: Amplitude A =0.1m

Q: A mass-spring system oscillates on a frictionless horizontal surface in simple harmonic motion with…

Q: A 0.1 kg object oscillates as a simple harmonic motion along the x-axis with a frequency f = 3.185…

A: we know that,

Q: A mass-spring system oscillates on a frictionless horizontal surface in simple harmonic motion with…

Q: A horizontal spring is attached to a wall at one end and a mass of 5.3 kg on the other end. The…

A: Given data: mass of the object attached to spring, m = 5.3 kgextension of spring, x = 0.88 m Time…

Q: A 1.92kg block on a horizontal frictionless surface is attached to an ideal spring whose force…

Q: A mass-spring system oscillates on a frictionless horizontal surface in simple harmonic motion with…

Q: A block of mass 2.8x105 kg is attached to a horizontal spring and the system oscillates with a…

A: The position of mass in simple harmonic motion is given by: x=Asinωt v=Aωcosωt =ωA2-A2sin2ωt…

Q: A mass is attached to a spring, pulled down an amount x below the equilibrium position, and…

Q: 1. A 10 kg mass vibrates according to the equation: (t) = (0.42m) sin 7.4?, where x is in meters and…

Q: A 0.1 kg object oscillates as a simple harmonic motion along the x -axis with a frequency f = 3.185…

Q: A block of mass m= 3.50 kg oscillates on a flat horizontal frictionless surface, under the action of…

A: Given Data: The mass of the block is: m=3.50 kg The elastic constant of spring 1 is: k1=1.00 N/m The…

Q: A mass-spring system oscillates on a frictionless horizontal surface in simple harmonic motion with…

Q: A mass on a spring, moving with simple harmonic motion, vibrates with a frequency of 4.0 Hz and an…

Q: A 5.00 kg object on a horizontal frictionless surface is attached to a spring with k= 1000 N/m. The…

Concept explainers

Special Relativity

The theory of special relativity discusses how space and time are related to objects traveling along a straight line at a constant speed. Simply stated, as an object reaches the speed of light, its mass becomes infinite and it is unable to move faster than light. This interstellar speed limit has been the topic of much debate in astronomy, and also in science fiction when people consider how to fly over large distances.

Question

need help with d-i

A compact, dense object with a mass of 4.10 kg is attached to a spring and is able to oscillate horizontally with negligible friction. The object is pulled to a distance
of 0.200 m from its equilibrium position, held in place with a force of 29.0 N, and then released from rest. It then oscillates in simple harmonic motion. (The object
oscillates along the x-axis, where x =
O is the equilibrium position.)
(a) What is the spring constant (in N/m)?
N/m
(b) What is the frequency of the oscillations (in Hz)?
Hz
(c) What is the maximum speed of the object (in m/s)?
m/s
(d) At what position(s) (in m) on the x-axis does the maximum speed occur?
X = +
(e) What is the maximum acceleration of the object? (Enter the magnitude in m/s2.)
m/s?
(f) At what position(s) (in m) on the x-axis does the maximum acceleration occur?
X = ±
m
(g) What is the total mechanical energy of the oscillating spring-object system (in J)?
(h) What is the speed of the object (in m/s) when its position is equal to one-third of the maximum displacement from equilibrium?
m/s
(i)
What is the magnitude of the acceleration of the object (in m/s) when its position is equal to one-third of the maximum displacement from equilibrium?
m/s?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Trending now

This is a popular solution!

Step by step

Solved in 6 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

Which of the following statements is not true regarding a massspring system that moves with simple harmonic motion in the absence of friction? (a) The total energy of the system remains constant. (b) The energy of the system is continually transformed between kinetic and potential energy. (c) The total energy of the system is proportional to the square of the amplitude. (d) The potential energy stored in the system is greatest when the mass passes through the equilibrium position. (e) The velocity of the oscillating mass has its maximum value when the mass passes through the equilibrium position.
A 200-g block is attached to a horizontal spring and executes simple harmonic motion with a period of 0.250 s. The total energy of the system is 2.00 J. Find (a) the force constant of the spring and (b) the amplitude of the motion.
A blockspring system oscillates with an amplitude of 3.50 cm. The spring constant is 250 N/m and the mass of the block is 0.500 kg. Determine (a) the mechanical energy of the system, (b) the maximum speed of the block, and (c) the maximum acceleration.
When a block of mass M, connected to the end of a spring of mass ms = 7.40 g and force constant k, is set into simple harmonic motion, the period of its motion is T=2M+(ms/3)k A two-part experiment is conducted with the use of blocks of various masses suspended vertically from the spring as shown in Figure P15.76. (a) Static extensions of 17.0, 29.3, 35.3, 41.3, 47.1, and 49.3 cm are measured for M values of 20.0, 40.0, 50.0, 60.0, 70.0, and 80.0 g, respectively. Construct a graph of Mg versus x and perform a linear least-squares fit to the data. (b) From the slope of your graph, determine a value for k for this spring. (c) The system is now set into simple harmonic motion, and periods are measured with a stopwatch. With M = 80.0 g, the total time interval required for ten oscillations is measured to be 13.41 s. The experiment is repeated with M values of 70.0, 60.0, 50.0, 40.0, and 20.0 g, with corresponding time intervals for ten oscillations of 12.52, 11.67, 10.67, 9.62, and 7.03 s. Make a table of these masses and times. (d) Compute the experimental value for T from each of these measurements. (e) Plot a graph of T2 versus M and (f) determine a value for k from the slope of the linear least-squares fit through the data points. (g) Compare this value of k with that obtained in part (b). (h) Obtain a value for ms from your graph and compare it with the given value of 7.40 g.
A simple harmonic oscillator has amplitude A and period T. Find the minimum time required for its position to change from x = A to x = A/2 in terms of the period T.
A grandfather clock has a pendulum length of 0.7 m and mass bob of 0.4 kg. A mass of 2 kg falls 0.8 m in seven days to keep the amplitude (from equilibrium) of the pendulum oscillation steady at 0.03 rad. What is the Q of the system?
Show that angular frequency of a physical pendulum phy=mgrCM/I (Eq. 16.33) equals the angular frequency of a simple pendulum smp=g/, (Eq. 16.29) in the case of a particle at the end of a string of length .
A 500-kg object attached to a spring with a force constant of 8.00 N/m vibrates in simple harmonic motion with an amplitude of 10.0 cm. Calculate the maximum value of its (a) speed and (b) acceleration, (c) the speed and (d) the acceleration when the object is 6.00 cm from the equilibrium position, and (e) the time interval required for the object to move from x = 0 to x = 8.00 cm.
A 50.0-g object connected to a spring with a force constant of 35.0 N/m oscillates with an amplitude of 4.00 cm on a frictionless, horizontal surface. Find (a) the total energy of the system and (b) the speed of the object when its position is 1.00 cm. Find (c) the kinetic energy and (d) the potential energy when its position is 3.00 cm.
If a simple pendulum oscillates with small amplitude and its length is doubled, what happens to the frequency of its motion? (a) It doubles. (b) It becomes 2 times as large. (c) It becomes half as large. (d) It becomes 1/2 times as large. (e) It remains the same.
In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression x=5.00cos(2t+6) where x is in centimeters and t is in seconds. At t = 0, find (a) the position of the piston, (b) its velocity, and (c) its acceleration. Find (d) the period and (e) the amplitude of the motion.
A 1.00-kg glider attached to a spring with a force constant of 25.0 N/m oscillates on a frictionless, horizontal air track. At t = 0, the glider is released from rest at x = 3.00 cm (that is, the spring is compressed by 3.00 cm). Find (a) the period of the gliders motion, (b) the maximum values of its speed and acceleration, and (c) the position, velocity, and acceleration as functions of time.