Simple Harmonic Motion

VOCAB

100

The maximum displacement from the equilibrium

position.

Amplitude

200

There is some force acting to stop the SHM.

Damping

300

The time it takes for the SHO to complete 1 revolution

Period of oscillation

400

The number of oscillations per second.

Frequency of Oscillation

500

An object which periodically oscillates about a fixed point known as the equilibrium

Simple Harmonic Oscillator

Equations

100

What is this formula used for: T=1/f

Period/Frequency

200

What is this equation used for: T=2π√ m/k

Period of a spring

300

What is this equation used for: T=2π√l/g

Period of a pendulum 

400

At time t=0, an object is released from rest at position x=+x_max and undergoes simple harmonic motion along the x-axis about the equilibrium position of x=0. The period of oscillation of object is T. Which of the following equations is equal to the object's position at time t=T/8?

a. x_max/8

b. x_max/2

c. x_maxcos(pi/8)

d.x_maxcos(pi/4)

d. x_maxcos(pi/4)

500

A block is released from rest on a track that consists of two ramps that are at the same small angle to the horizontal. The block makes a smooth transition from one ramp to another, and friction between the block and the track is negligible. The block slides back and forth along the track. Will the block undergo SHM? Why or why not?

a. yes because the motion of the block is periodic

b. yes, because the restoring force exerted by the component of the gravitational force parallel to the ramp is always opposite the direction of the displacement of the block from equilibrium.

c. no, because the average net force on the block over one complete oscillation is zero.

d. No, because the restoring force exerted by the component of the gravitational force parallel to the ramp is not proportional to the block's displacement from equilibrium. 

d. No, because the restoring force exerted by the component of the gravitational force parallel to the ramp is not proportional to the block's displacement from equilibrium.

Springs

100

A block of mass m ocillates on a spring with frequency f. Which of the following expressions is equal to the spring constant of the spring.

a. 2πm/f^2      b. 4π^2m/f^2    c.2πmf^2      d.4π^2mf^2

d. 4π^2mf^2

200

A block is attached to a horizontal spring. The block is held so the spring is stretched and the block is released from rest, undergoing simple harmonic motion with a frequency of 2 Hz. How long after release will the block first reach a point where it is momentarily at rest?

a. 0.25s

b. 0.50s

c. 1.0s

d. 2.0s

a. 0.25s

300

An object with mass m attached to a horizontal spring with spring constant k undergoes simple harmonic motion with A and period T. Which of the following expressions is equal to the maximum speed of the block? 

a. 4A/T

b. √k/m(A)

c. k/m(A)^2

d. 1/2(kA)^2

b.√k/m(A)

400

A platform of mass 2.0kg rests on a vertical spring with a spring constant k=250N/m. The equilibrium length of the spring is L1. A ball of clay of mass 0.5kg is then placed on the platform and the system is allowed to come to rest. The new equilibrium length of the spring is L2. What is the difference L1-L2 between the equilibrium lengths of the spring? 

A. 0.02m    B. 0.06m      C. 0.08m        D.0.10m

A. 0.02m

500

A block attached to a spring is held at position x=0 and released. The block then undergoes simple harmonic motion along the x-axis. The force exerted on the block by the spring as a function of the block's position x is represented by the graph. Which of the following positions, if any, corresponds to the equilibrium position of the spring-block system?

a.0.om

b. 0.50m

c. 1.0m

d. there is no equilibrium position because the force is nonzero at x=0.

a. 0.0m

Pendulum/Springs 2

100

A simple pendulum near the surface of Earth has a period T_E. The same pendulum is transported to the surface of the Moon, where the acceleration due to gravity is approximately g/6, and the pendulum has a period T_M. The ratio of T_M:T_E is most nearly.

a. 1:6

b. 1:√ 6

c. √6:1

d. 6:1

c. √6:1

200

A block of mass 0.40kg attached to a horizontal spring is undergoing simple harmonic motion along a horizontal surface. The maximum acceleration of the block has a magnitude of 1.5 m/s² and occurs when the block is displaced by a distance of 0.20m from its equilibrium position. The spring constant of the spring is most nearly

a. 0.12 N/m

b. 0.60 N/m

c. 3.0 N/m

d. 7.5 N/m

c. 3.0 N/m

300

One end of a horizontal spring with spring constant 100 N/m is attached to a block of mass 0.50 kg, and the other end is attached to a wall. The block can slide with negligible friction along the x-axis on a horizontal surface. When the block is at position x=0.75m, the spring is at its unstreched length. From which of the following positions can the block be released and have a maximum acceleration with magnitude 20 m/s².

a. 0.10m

b. 0.20m

c. 0.65m

d. 0.95m

c. 0.65m

400

A block attached to a horizontal spring undergoes shm along a horizontal surface. When the block is at its maximum displacement, the force exerted on the block by the spring has magnitude F_A, and when the block is at its equilibrium position, the force exerted on the block by the spring has a magnitude F_eq. Which of the following correctly compares F_A and F_eq , and provides a valid justification.

a. F_A = F_eq because the force is zero when the block is at its equilibrium position and when it is at its maximum displacement. 

b. F_A = F_eq because the force on the block is constant throughout the block's motion

c. F_A > F_eq because the speed of the block is a maximum when the displacement is a max and zero when the displacement is zero.

d. F_A > F_eq because the force is zero at the equilibrium position and a max and max displacement

d. F_A > F_eq because the force is zero at the equilibrium position and a max and max displacement

500

A block of mass 2.0kg on a horizontal surface is attached to one end of a spring with spring constant 30 N/m. The other end of the spring is attached to a wall. There is negligible friction between the block and the surface. The block is displaced a distance 0.1 m from equilibrium and released from rest, after which the block undergoes simple harmonic motion. The magnitude of the max acceleration of the block is almost nearly

a. 10m/s²

b. 6.0m/s²

c. 3.0m/s²

d.1.5 m/s²

d. 1.5 m/s²

Symbols

100

What does this symbol mean: A

amplitude

200

ω what does this symbol mean.

angular frequency

300

T what does this symbol mean?

period

400

Which of the following must be true for an object undergoing simple harmonic motion?

a. the force exerted on the object is in the direction of the object's displacement

b. the magnitude of the force exerted on the object is proportional to the object's displacement from equilibrium.

c. the magnitude of the acceleration of the object is at its maximum value when the object is at its equilibrium position.

d. the speed of the object is at its maximum value when the object is at its maximum displacement.

b. the magnitude of the force exerted on the object is proportional to the object's displacement from equilibrium.

500

Which of the following types of motion can be described as simple harmonic motion?

a. an ice cube sliding down one side of a curved bowl, past the bottom and back up the other side

b. a ball rolling down a ramp and back up another ramp where the angle of both ramps with the vertical is the same

c. a cart sliding back and forth on a surface while attached to a spring

d. a dropped ball that collides elastically with the floor and returns to its initial height

c. a cart sliding back and forth on a surface while attached to a spring