Springs & pendulums worksheet with answers

Free printable Springs & pendulums worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
1.6 kgk

A 1.6 kg mass on a spring makes 25 complete oscillations in 7 s. Find the frequency f of the oscillation.

m = 1.6 kgN = 25t = 7 s
f = Hz
2.Easy
3.8 kgk

A 3.8 kg mass on a spring makes 10 complete oscillations in 14 s. Find the frequency f of the oscillation.

m = 3.8 kgN = 10t = 14 s
f = Hz
3.Medium
L = 1.2 m

A simple pendulum has a length of 1.2 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.2 mg = 9.81 m/s²
T = s
4.Medium
L = 0.7 m

A simple pendulum has a length of 0.7 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.7 mg = 9.81 m/s²
T = s
5.Hard
t (s)x (cm)t = ?8.8

A body oscillates in simple harmonic motion with period 1.3 s and amplitude 11 cm. What is the shortest time t it needs to move from its maximum displacement of 11 cm to a displacement of 8.8 cm?

T = 1.3 sA = 11 cmx = 8.8 cm
t = s
6.Hard
1.1 kgk = 170 N/mA = 2 cm

A 1.1 kg mass on a spring with k = 170 N/m is pulled 2 cm from equilibrium and released. Find its maximum acceleration amax.

m = 1.1 kgk = 170 N/mA = 2 cm
amax = m/s²

Answer key

  1. 1. f = 3.571 Hz
  2. 2. f = 0.7143 Hz
  3. 3. T = 2.198 s
  4. 4. T = 1.678 s
  5. 5. t = 0.1331 s
  6. 6. amax = 3.091 m/s²

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