Physics Practice Test: Simple Harmonic Motion, Springs and Pendulums
- Simple Harmonic Motion
- 10 questions
- 13 minutes
This test covers springs, pendulums and other systems that swing back and forth. Use g = 9.8 m/s². Tip: a pendulum’s period depends on its length and on g, not on its mass.
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Question 1
A spring with a spring constant of 200 N/m is stretched 0.15 m from its natural length. How much force does the spring exert?
Correct answer: A
Hooke’s law gives F = kx = 200 × 0.15 = 30 N. Dividing 200 by 0.15 gives about 1,333 N, which is the wrong operation.
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Question 2
A 0.50 kg mass hangs on a spring with k = 50 N/m and bounces up and down. What is the period of its motion?
Correct answer: A
T = 2π√(m/k) = 2π√(0.50/50) = 2π × 0.10 ≈ 0.63 s. The value 1.6 is the frequency in hertz (1 ÷ 0.63), not the period, and 0.10 s forgets the 2π.
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Question 3
A pendulum’s length is made four times longer. What happens to its period (for small swings)?
Correct answer: D
The period is T = 2π√(L/g), so it depends on the square root of the length: √4 = 2. Assuming the period grows in direct proportion to length gives four times, which is too much.
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Question 4
Two pendulums have the same length. One bob has a mass of 1 kg and the other 2 kg. Both swing with small angles. How do their periods compare?
Correct answer: B
Mass does not appear in T = 2π√(L/g): a heavier bob needs more force to accelerate, but gravity pulls on it harder by the same factor. Only length and g decide the period.
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Question 5
Where is a swinging pendulum bob moving the fastest?
Correct answer: C
At the lowest point, all of the potential energy has turned into kinetic energy, so the speed is greatest. At the highest points the bob stops for an instant before swinging back.
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Question 6
A mass on a spring is at its maximum displacement from equilibrium. Which statement is true at this point?
Correct answer: C
At the turning point the mass stops for an instant, but the spring is stretched the most, so the restoring force and the acceleration are largest. At equilibrium it is the other way round.
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Question 7
A child on a swing makes 20 complete swings in 8.0 s. What is the frequency of the swing?
Correct answer: D
Frequency is the number of cycles per second: 20 ÷ 8.0 = 2.5 Hz. The value 0.40 is the period in seconds (8.0 ÷ 20), not the frequency.
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Question 8
A spring with k = 400 N/m is compressed 0.10 m. How much elastic potential energy does it store?
Correct answer: B
PE = ½kx² = ½ × 400 × (0.10)² = ½ × 400 × 0.010 = 2.0 J. Forgetting the ½ gives 4.0 J, and using kx gives 40, which is a force in newtons, not an energy.
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Question 9
A 2.0 kg block on a frictionless surface is attached to a spring with k = 200 N/m. It oscillates with an amplitude of 0.10 m. What is its maximum speed?
Correct answer: A
All the spring energy at the end, ½kA², becomes kinetic energy at the middle, ½mv², so v = A√(k/m) = 0.10 × √100 = 1.0 m/s. Forgetting to multiply by the amplitude gives 10 m/s.
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Question 10
How long should a simple pendulum be to have a period of 2.0 s on Earth?
Correct answer: C
Solving T = 2π√(L/g) for L gives L = gT² ÷ 4π² = 9.8 × 4.0 ÷ 39.5 ≈ 0.99 m. A 2.0 m pendulum would have a period of about 2.8 s.
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