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
3.2 kgk

A 3.2 kg mass on a spring makes 50 complete oscillations in 57 s. Find the frequency f of the oscillation.

m = 3.2 kgN = 50t = 57 s
f = Hz
2.Easy
2.9 kgk = ?

A 2.9 kg mass on a spring makes 50 complete oscillations in 14 s. Find the spring stiffness k.

m = 2.9 kgN = 50t = 14 s
k = N/m
3.Medium
t (s)x (cm)0.85 s

A 0.3 kg mass on a spring with k = 130 N/m is pulled 3 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.85 s (with sign).

m = 0.3 kgk = 130 N/mA = 3 cmt = 0.85 s
x = cm
4.Medium
L = 0.6 m

A simple pendulum has a length of 0.6 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.6 mg = 9.81 m/s²
T = s
5.Hard
mk = 130 N/mA = 16 cmx = 12 cm

A mass on a spring with k = 130 N/m oscillates on a frictionless surface with an amplitude of 16 cm. Find its kinetic energy K when it is 12 cm from equilibrium.

k = 130 N/mA = 16 cmx = 12 cm
K = J
6.Hard
3.2 kgk = 130 N/mA = 19 cm

A 3.2 kg mass on a spring with k = 130 N/m is pulled 19 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.2 kgk = 130 N/mA = 19 cm
amax = m/s²

Answer key

  1. 1. f = 0.8772 Hz
  2. 2. k = 1460 N/m
  3. 3. x = 1.211 cm
  4. 4. T = 1.554 s
  5. 5. K = 0.728 J
  6. 6. amax = 7.719 m/s²

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