Practice Simple Harmonic Motion in Physics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

Oscillatory motion where the restoring force is proportional to displacement from equilibrium, producing sinusoidal position over time.

A spring or pendulum that bounces back and forth in a smooth, repeating pattern.

Showing a random 20 of 50 problems.

Example 1

medium
A pendulum has period T=2 sT = 2 \text{ s}. Find its length on Earth. Use g=9.8 m/s2g = 9.8 \text{ m/s}^2.

Example 2

easy
A mass-spring system has m=0.25 kgm = 0.25 \text{ kg} and k=100 N/mk = 100 \text{ N/m}. Find the period of oscillation.

Example 3

easy
What is the defining property of the restoring force in SHM?

Example 4

challenge
A 0.5 kg mass on a spring (k=50 N/mk = 50 \text{ N/m}) has amplitude 0.4 m. Find its maximum kinetic energy.

Example 5

medium
A mass of 0.4 kg0.4 \text{ kg} oscillates on a spring with k=100 N/mk = 100 \text{ N/m} and amplitude A=0.05 mA = 0.05 \text{ m}. Find the maximum speed.

Example 6

medium
A spring with k=200 N/mk = 200 \text{ N/m} is compressed 0.1 m. Find the elastic PE stored. (PE=12kx2PE = \frac{1}{2}kx^2)

Example 7

easy
A mass-spring system has m=2 kgm = 2 \text{ kg} and k=8 N/mk = 8 \text{ N/m}. Find the period. (T=2πm/kT = 2\pi\sqrt{m/k})

Example 8

medium
A mass-spring system has m=0.5 kgm = 0.5 \text{ kg} and k=32 N/mk = 32 \text{ N/m}. Find its frequency. (f=12πk/mf = \frac{1}{2\pi}\sqrt{k/m})

Example 9

medium
A pendulum on the Moon (g=1.6g = 1.6) has length 1 m. Find its period. (T=2πL/gT = 2\pi\sqrt{L/g})

Example 10

challenge
A 0.2 kg0.2 \text{ kg} mass on a spring with k=50 N/mk = 50 \text{ N/m} is set into SHM with amplitude 0.06 m0.06 \text{ m}. At what displacement is half the energy kinetic and half potential?

Example 11

challenge
Two springs k1=100k_1 = 100 and k2=300 N/mk_2 = 300 \text{ N/m} connect in parallel to a 2 kg mass (effective k=k1+k2k = k_1 + k_2). Find the period.

Example 12

easy
Where in its motion is a SHM oscillator moving fastest?

Example 13

medium
A SHM oscillator has A=0.1 mA = 0.1 \text{ m} and ω=10 rad/s\omega = 10 \text{ rad/s}. Find the maximum acceleration.

Example 14

hard
A 0.5 kg0.5 \text{ kg} mass on a spring (k=200 N/mk = 200 \text{ N/m}) oscillates with amplitude 0.04 m0.04 \text{ m}. What is the total energy of the system, and what is the speed when the displacement is 0.02 m0.02 \text{ m}?

Example 15

hard
A 1 kg1 \text{ kg} mass on a spring (k=100 N/mk = 100 \text{ N/m}) has amplitude 0.10 m0.10 \text{ m}. Find its speed when x=0.06 mx = 0.06 \text{ m}.

Example 16

easy
Does increasing the amplitude of a mass-spring SHM change its period?

Example 17

medium
A 0.2 kg mass on a spring (k=80 N/mk = 80 \text{ N/m}) oscillates. How many full cycles occur in 10 s?

Example 18

medium
A pendulum has period 2 s on Earth (g=9.8g = 9.8). To double its period to 4 s, by what factor must its length change?

Example 19

easy
A pendulum's period is 4 s. What is its frequency? (f=1/Tf = 1/T)

Example 20

medium
A 1 kg mass on a spring (k=100 N/mk = 100 \text{ N/m}) has amplitude 0.2 m. Find its maximum speed. (ω=k/m\omega = \sqrt{k/m}, vmax=ωAv_{max} = \omega A)
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