Question 1

A mass $$m$$ attached to a spring with spring constant $$k$$ oscillates in simple harmonic motion. What is the angular frequency $$\omega of $$the motion?

Accepted Answer

$$\omega = \sqrt{\dfrac{k}{m}}$$

Question 2

Which of the following is the general solution for the position $$x(t) of a $$mass undergoing simple harmonic motion?

Accepted Answer

$$x(t) = A \cos(\omega t + \phi)$$

Question 3

A block of mass $$m is $$attached to a spring and oscillates with amplitude $$A. At $$what position $$x is $$the kinetic energy equal to the potential energy?

Accepted Answer

$$x = \pm \dfrac{A}{\sqrt{2}}$$

Question 4

If the amplitude of a simple harmonic oscillator is doubled, how does the total mechanical energy change?

Accepted Answer

It increases by a factor of 4.

Question 5

A mass $$m$$ oscillates on a spring with amplitude $$A$$ and angular frequency $$\omega. $$What is the maximum velocity $$v_{max} of $$the mass?

Accepted Answer

$$v_{max} = \omega A$$

Question 6

A block is released from rest at $$x = 0.10\ \mathrm{m} in a $$spring-mass system. What is the phase constant $$\phi$$?

Accepted Answer

$$\phi = 0$$

Question 7

At what position is the potential energy of a spring-mass system in SHM the greatest?

Accepted Answer

At $$x = \pm A$$

Question 8

A mass $$M$$ oscillates in SHM with amplitude $$A_1$$ and velocity $$v_1 at $$equilibrium. A putty of mass $$m$$ lands and sticks to it at $$x=0. $$What is the velocity $$v_2$$ immediately after the collision?

Accepted Answer

$$v_2$$ = \dfrac{M}{M + m} $$v_1$$

Question 9

After the putty sticks to the block in the previous question, what is the new amplitude $$A_2 of $$the SHM?

Accepted Answer

$$A_2$$ = \dfrac{M}{M + m} $$A_1$$

Question 10

To double the total energy of a spring-mass system in SHM, by what factor should the amplitude be increased?

Accepted Answer

$$\sqrt{2}$$

Question 11

A block attached to a spring is moving to the right at $$x = 0.10\ \mathrm{m} at$$ $$t = 0. $$What is the relationship between the amplitude $$A$$ and the initial position?

Accepted Answer

$$A = \dfrac{0.10\ \mathrm{m}}{\cos(\phi)} \u003e 0.10\ \mathrm{m}$$

Question 12

Which of the following best describes the energy distribution at $$x = 0$$ for a spring-mass system in SHM?

Accepted Answer

All energy is kinetic; potential energy is zero.

Question 13

What is the expression for the velocity $$v(x) of a $$mass in SHM as a function of position $$x$$?

Accepted Answer

$$v(x) = \pm \sqrt{\dfrac{k}{m}(A^2$ - x^2$)}$$

Question 14

If a block is at $$x = A in $$SHM, what is its velocity?

Accepted Answer

$$v = 0$$

Question 15

Which of the following statements about the frequency $$\omega of a $$spring-mass system in SHM is correct?

Accepted Answer

$$\omega is $$independent of the amplitude $$A.$$

Question 16

A block of mass $$m$$ oscillates on a spring with spring constant $$k. $$What is the period $$T of $$the motion?

Accepted Answer

$$T = 2\pi \sqrt{\dfrac{m}{k}}$$

Question 17

At which position(s) is the energy of a spring-mass system in SHM half kinetic and half potential?

Accepted Answer

$$x = \pm \dfrac{A}{\sqrt{2}}$$

Question 18

A block attached to a spring is at $$x = 0.10\ \mathrm{m}$$ and moving to the right at $$t = 0. $$What is the sign of the phase constant $$\phi$$?

Accepted Answer

$$\phi \u003c 0$$

Question 19

Which of the following is true about energy conservation in a totally inelastic collision involving a mass in SHM and a putty?

Accepted Answer

The energy of the oscillator is not conserved before and after the collision.

Periodic Motion I: Simple Harmonic Motion (SHM) – Study Notes

Study Guide - Practice Questions

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