## SAT Physics Subject Test

## Chapter 7 Oscillations

### Chapter 7 Review Questions

See __Chapter 17__ for solutions.

__1__. Characteristics of simple harmonic motion include which of the following?

I. The acceleration is constant.

II. The restoring force is proportional to the displacement.

III. The frequency is independent of the amplitude.

(A) II only

(B) I and II only

(C) I and III only

(D) II and III only

(E) I, II, and III

__2__. A block attached to an ideal spring undergoes simple harmonic motion. The acceleration of the block has its maximum magnitude at the point where

(A) the speed is the maximum

(B) the potential energy is the minimum

(C) the speed is the minimum

(D) the restoring force is the minimum

(E) the kinetic energy is the maximum

__3__. A block attached to an ideal spring undergoes simple harmonic motion about its equilibrium position (*x* = 0) with amplitude *A*. What fraction of the total energy is in the form of kinetic energy when the block is at position *x* = *A* ?

(A)

(B)

(C)

(D)

(E)

__4__. A student measures the maximum speed of a block undergoing simple harmonic oscillations of amplitude *A* on the end of an ideal spring. If the block is replaced by one with twice the mass but the amplitude of its oscillations remains the same, then the maximum speed of the block will

(A) decrease by a factor of 4

(B) decrease by a factor of 2

(C) decrease by a factor of

(D) remain the same

(E) increase by a factor of 2

__5__. A spring–block simple harmonic oscillator is set up so that the oscillations are vertical. The period of the motion is *T*. If the spring and block are taken to the surface of the moon, where the gravitational acceleration is of its value here, then the vertical oscillations will have a period of

(A)

(B)

(C)

(D) T

(E) T

__6__. A linear spring of force constant *k* is used in a physics lab experiment. A block of mass *m* is attached to the spring and the resulting frequency, *f*, of the simple harmonic oscillations is measured. Blocks of various masses are used in different trials, and in each case, the corresponding frequency is measured and recorded. If *f*^{2} is plotted versus 1/*m*, the graph will be a straight line with slope

(A) 4π^{2}/*k*^{2}

(B) 4π^{2}/*k*

(C) 4π^{2}*k*

(D) *k*/(4π^{2})

(E) *k*^{2}/(4π^{2})

__7__. A block of mass *m* = 4 kg on a frictionless, horizontal table is attached to one end of a spring of force constant *k* = 400 N/m and undergoes simple harmonic oscillations about its equilibrium position (*x* = 0) with amplitude *A* = 6 cm. If the block is at *x* = 6 cm at time *t* = 0, then which of the following equations (with *x* in centimeters and *t* in seconds) gives the block”s position as a function of time?

(A) *x* = 6 sin(10*t* + π)

(B) *x* = 6 sin(10π*t*)

(C) *x* = 6 sin(10π*t* – π)

(D) *x* = 6 sin(10*t*)

(E) *x* = 6 sin(10*t* –π)

__8__. A student is performing a lab experiment on simple harmonic motion. She has two different springs (with force constants *k*_{1} and *k*_{2}) and two different blocks (of masses *m*_{1} and *m*_{2}). If *k*_{1} = 2*k*_{2} and *m*_{1} = 2*m*_{2}, which of the following combinations would give the student thespring–block simple harmonic oscillator with the shortest period?

(A) The spring with force constant *k*_{1} and the block of mass *m*_{1}

(B) The spring with force constant *k*_{1} and the block of mass *m*_{2}

(C) The spring with force constant *k*_{2} and the block of mass *m*_{1}

(D) The spring with force constant *k*_{2} and the block of mass *m*_{2}

(E) All the combinations above would give the same period.

__9__. A simple pendulum swings about the vertical equilibrium position with a maximum angular displacement of 5 and period *T*. If the same pendulum is given a maximum angular displacement of 10°, then which of the following best gives the period of the oscillations?

(A)

(B)

(C) *T*

(D) *T*

(E) 2*T*

__10__. A simple pendulum of length *L* and mass *m* aswings about the vertical equilibrium position (*θ* = 0) with a maximum angular displacement of *θ*_{max}. What is the tension in the connecting rod when the pendulum”s angular displacement is *θ* = *θ*_{max} ?

(A) *mg* sin*θ*_{max}

(B) *mg* cos*θ*_{max}

(C) *mgL* sin*θ*_{max}

(D) *mgL* cos*θ*_{max}

(E) *mgL*(1 – cos*θ*_{max})

**Keywords**

simple harmonic motion

Hooke”s law

spring (or force) constant

equilibrium position

restoring force

ideal (or linear) springs

oscillate

elastic potential energy

amplitude

cycle

period

frequency

hertz (Hz)

effective spring constant

simple pendulum

phase

**Summary**

· When a spring is stretched or compressed horizontally, a force is created as the spring tries to return to its equilibrium position. The force it exerts in response is given by Hooke”s law: **F**_{s} = −*kx*.

· During oscillation, the force on the block when it is at equilibrium is zero, while the speed is at a maximum.

· At amplitude, when displacement from equilibrium is largest, the force and magnitude of acceleration are both at their maximum.

· The trading off of energy between potential and kinetic causes oscillations.

· Each cycle of oscillation occurs in the same amount of time.

1. The amount of time it takes to complete a cycle is called a period and is expressed in seconds per cycle.

2. The number of cycles that can be completed in a unit of time is called the frequency of the oscillations and is expressed in cycles per second.

· The forces at play in the vertical motion of a spring are very similar to those in horizontal motion. The only difference is that, due to gravity, the vertical motion of a spring equilibrium is not at the spring”s natural length.

· For an object moving with simple harmonic motion, the period and frequency are independent of the amplitude.

· Displacement of a simple pendulum is measured by the angle that it makes with the vertical. A pendulum”s restoring force is provided by gravity and is proportional to the displacement.

· For small angles, a pendulum exhibits simple harmonic motion.

· The period and frequency of a pendulum do not depend on the mass.