# Worksheet: Simple Harmonic Motion

In this worksheet, we will practice analyzing the simple harmonic motion of an object.

Q1:

A mass on a spring oscillates with a period of 0.8 s and an amplitude of 12 cm. At , it is 6 cm to the left of equilibrium and moving to the left. What is the position of the mass at time ?

• A12 cm to the right of equilibrium
• B24 cm to the right of equilibrium
• C3 cm to the right of equilibrium
• D10 cm to the right of equilibrium
• E6 cm to the right of equilibrium

Q2:

A particle is moving along a straight line with simple harmonic motion. Its maximum acceleration is 10 ms−2 and its maximum speed is 3 ms−1. Calculate the amplitude of the motion.

• A m
• B m
• C m
• D m
• E m

Q3:

A particle of mass 0.4 kg is moving along a straight line with simple harmonic motion. The distance between and a fixed point on the line is meters at seconds. The force acting on has a magnitude of and acts in the direction opposite to the motion. Find the period of the motion.

• A
• B
• C
• D

Q4:

A 6 kg mass attached to a spring is observed to oscillate with a period of 3 s. What is the period of oscillation if a 8 kg mass is attached to the spring?

• A s
• B s
• C s
• D s
• E s

Q5:

A particle of mass 15 g moves in simple harmonic motion with a frequency of 3 Hz and an amplitude of 4 cm.

Determine the period of the motion.

• A s
• B4 s
• C3 s
• D s
• E6 s

Find the maximum speed of the particle.

• A cm/s
• B4 cm/s
• C cm/s
• D cm/s
• E cm/s

Find the maximum acceleration of the particle.

• A cm/s2
• B4 cm/s2
• C cm/s2
• D cm/s2
• E cm/s2

Q6:

A simple harmonic oscillator takes 15 s to undergo five complete vibrations. Find the angular frequency in radians per second.

• A
• B
• C
• D
• E

Q7:

A particle vibrates along the with a frequency of 5 Hz. Determine the time taken by the particle to reach the maximum positive displacement eleven times, starting from the equilibrium position while moving in the positive direction.

Q8:

A mass on a spring oscillates with a period of 0.8 s and an amplitude of 8 cm. At , it is 4 cm to the left of equilibrium and moving to the left. What is the magnitude of the velocity of the mass at time ?

• A cm/s
• B cm/s
• C cm/s
• D cm/s
• E cm/s

Q9:

The displacement of a particle as a function of time is given by , where is measured in meters and in seconds.

Determine the period of the motion.

• A2 s
• B4 s
• C1 s
• D0.25 s
• E0.5 s

Determine the amplitude of the motion.

Determine the phase constant.

• A
• B
• C
• D
• E

Q10:

A spring stretches by 4.9 cm when a 10 g mass is hung from it. Calculate the period of motion when a 20 g mass attached to this spring oscillates in simple harmonic motion.

• A
• B
• C
• D
• E