A mass m on a spring with spring constant k oscillates with Simple Harmonic Motion. Assume m and k are both known in base SI units. The exact position of the harmonic oscillator is described by this function. All quantities are expressed in base Sl units: x(t) = cos(3t + T4) This is a multi-select question, you must select 2 correct answers to receive full credit. Question #1: What is the period of the oscillation? Question #2: What is the total distance traveled by the oscillator during one full period? (Hint: this is not asking for the displacement) | The period of the oscillation is 3r [s] | The period of the oscillation is 3 [s] | The period of the oscillation is 4 T [s] The period of the oscillation is 2/3 [s] The period of the oscillation is 3/4 n² [s] The total distance traveled during one full period is 0 [m] The total distance traveled during one full period is 1 [m] The total distance traveled during one full period is 2 [m] The total distance traveled during one full period is 4 [m]

A mass m on a spring with spring constant k oscillates with Simple Harmonic Motion. Assume m and k are both known in base SI units. The exact position of the harmonic oscillator is described by this function. All quantities are expressed in base Sl units: x(t) = cos(3t + T4) This is a multi-select question, you must select 2 correct answers to receive full credit. Question #1: What is the period of the oscillation? Question #2: What is the total distance traveled by the oscillator during one full period? (Hint: this is not asking for the displacement) | The period of the oscillation is 3r [s] | The period of the oscillation is 3 [s] | The period of the oscillation is 4 T [s] The period of the oscillation is 2/3 [s] The period of the oscillation is 3/4 n² [s] The total distance traveled during one full period is 0 [m] The total distance traveled during one full period is 1 [m] The total distance traveled during one full period is 2 [m] The total distance traveled during one full period is 4 [m]

Name: A mass m on a spring with spring constant k oscillates with Simple Ha
Uploaded: 2024-03-20T06:58:04.000Z
Channel: Bartleby
Description: A mass m on a spring with spring constant k oscillates with Simple Harmonic Motion.Assume m and k are both known in base SI units.The exact position of the harmonic oscillator is described by this function. Allquantities are expressed in base Sl uni

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 11OQ

See similar textbooks

Similar questions

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.
An object of mass m on a spring of stiffness k oscillates with an amplitude A about its equilibrium position. Suppose that m = 300 g, k = 10 N/m, and A = 10 cm. (a) Find the total energy. (b) Find the mechanical frequency of vibration of the mass. (c) Calculate the change in amplitude when the system loses one quantum of energy.
The total energy of a simple harmonic oscillator with amplitude 3.00 cm is 0.500 J. a. What is the kinetic energy of the system when the position of the oscillator is 0.750 cm? b. What is the potential energy of the system at this position? c. What is the position for which the potential energy of the system is equal to its kinetic energy? d. For a simple harmonic oscillator, what, if any, are the positions for which the kinetic energy of the system exceeds the maximum potential energy of the system? Explain your answer. FIGURE P16.73
A small object is attached to the end of a string to form a simple pendulum. The period of its harmonic motion is measured for small angular displacements and three lengths. For lengths of 1.000 m, 0.750 m, and 0.500 m, total time intervals for 50 oscillations of 99.8 s, 86.6 s, and 71.1s are measured with a stopwatch. (a) Determine the period of motion for each length. (b) Determine the mean value of g obtained from these three independent measurements and compare it with the accepted value. (c) Plot T2 versus L and obtain a value for g from the slope of your best-fit straight-line graph. (d) Compare the value found in part (c) with that obtained in part (b).
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.
Two masses m1 = 100 g and m2 = 200 g slide freely in a horizontal frictionless track and are connected by a spring whose force constant is k = 0.5 N/m. Find the frequency of oscillatory motion for this system.
We do not need the analogy in Equation 16.30 to write expressions for the translational displacement of a pendulum bob along the circular arc s(t), translational speed v(t), and translational acceleration a(t). Show that they are given by s(t) = smax cos (smpt + ) v(t) = vmax sin (smpt + ) a(t) = amax cos(smpt + ) respectively, where smax = max with being the length of the pendulum, vmax = smax smp, and amax = smax smp2.
The equations listed in Table 2.2 give position as a function of time, velocity as a function of time, and velocity as a function of position for an object moving in a straight line with constant acceleration. The quantity vxi appears in every equation. (a) Do any of these equations apply to an object moving in a straight line with simple harmonic motion? (b) Using a similar format, make a table of equations describing simple harmonic motion. Include equations giving acceleration as a function of time and acceleration as a function of position. State the equations in such a form that they apply equally to a blockspring system, to a pendulum, and to other vibrating systems. (c) What quantity appears in every equation?
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.
An automobile with a mass of 1000 kg, including passengers, settles 1.0 cm closer to the road for every additional 100 kg of passengers. It is driven with a constant horizontal component of speed 20 km/h over a washboard road with sinusoidal bumps. The amplitude and wavelength of the sine curve are 5.0 cm and 20 cm, respectively. The distance between the front and back wheels is 2.4 m. Find the amplitude of oscillation of the automobile, assuming it moves vertically as an undamped driven harmonic oscillator. Neglect the mass of the wheels and springs and assume that the wheels are always in contact with the road.
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.
An object of mass m moves in simple harmonic motion with amplitude 12.0 cm on a light spring. Its maximum acceleration is 108 cm/s2. Regard m as a variable. (a) Find the period T of the object. (b) Find its frequency f. (c) Find the maximum speed vmax of the object. (d) Find the total energy E of the objectspring system. (e) Find the force constant k of the spring. (f) Describe the pattern of dependence of each of the quantities T, f, vmax, E, and k on m.