A mass is placed on a frictionless, horizontal table. A spring (k = 100 N/m), which can be stretched or compressed, is placed on the table. A 9.00 kg mass is attached to one end of the spring, the other end is anchored to the wall. The equilibrium position is marked at zero. A student moves the mass out to x = 3.0 cm and releases it from rest at t = 0. The mass oscillates in SHM. (a) Determine the equations of motion. (Use the following as necessary: t. Round your coefficients to at least three significant figures. In your equations, let distance be in cm and time be in s. Do not include units in your answers.) position (in cm) x(t) = cm velocity (in cm/s) v(t) = cm/s acceleration (in cm/s?) a(t) = cm/s2 (b) Find the position (in cm), velocity (in cm/s), and acceleration (in cm/s2) of the mass at time t = 3.99 s. (Indicate the direction with the signs of your answers.) position cm velocity cm/s acceleration cm/s2
A mass is placed on a frictionless, horizontal table. A spring (k = 100 N/m), which can be stretched or compressed, is placed on the table. A 9.00 kg mass is attached to one end of the spring, the other end is anchored to the wall. The equilibrium position is marked at zero. A student moves the mass out to x = 3.0 cm and releases it from rest at t = 0. The mass oscillates in SHM. (a) Determine the equations of motion. (Use the following as necessary: t. Round your coefficients to at least three significant figures. In your equations, let distance be in cm and time be in s. Do not include units in your answers.) position (in cm) x(t) = cm velocity (in cm/s) v(t) = cm/s acceleration (in cm/s?) a(t) = cm/s2 (b) Find the position (in cm), velocity (in cm/s), and acceleration (in cm/s2) of the mass at time t = 3.99 s. (Indicate the direction with the signs of your answers.) position cm velocity cm/s acceleration cm/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 10P: A 1.00-kg glider attached to a spring with a force constant of 25.0 N/m oscillates on a...
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Concept explainers
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
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Transcribed Image Text:A mass is placed on a frictionless, horizontal table. A spring (k = 100 N/m), which can be stretched or compressed, is placed on the table. A 9.00 kg mass is attached to one end of the spring, the
other end is anchored to the wall. The equilibrium position is marked at zero. A student moves the mass out to x = 3.0 cm and releases it from rest at t = 0. The mass oscillates in SHM.
(a) Determine the equations of motion. (Use the following as necessary: t. Round your coefficients to at least three significant figures. In your equations, let distance be in cm and time be in s. Do
not include units in your answers.)
position (in cm)
x(t) =
cm
velocity (in cm/s)
v(t) =
cm/s
acceleration (in cm/s2)
a(t) =
cm/s2
(b) Find the position (in cm), velocity (in cm/s), and acceleration (in cm/s2) of the mass at time t = 3.99 s. (Indicate the direction with the signs of your answers.)
position
cm
velocity
cm/s
acceleration
cm/s2
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