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
4.5 kgk = ?

A 4.5 kg mass on a spring oscillates with a period of 2.1 s. Find the spring stiffness k.

m = 4.5 kgT = 2.1 s
k = N/m
2.Easy
0.1 kgk3.5 cm

Hanging a 0.1 kg mass on a spring stretches it by 3.5 cm. Use g = 9.81 m/s². The mass is then pulled down a little and released. Find the period T of its oscillation.

m = 0.1 kgx = 3.5 cmg = 9.81 m/s²
T = s
3.Medium
L = 2.2 m

A simple pendulum has a length of 2.2 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.2 mg = 9.81 m/s²
T = s
4.Medium
t (s)x (cm)0.3 s

A 2.5 kg mass on a spring with k = 300 N/m is pulled 6 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.3 s (with sign).

m = 2.5 kgk = 300 N/mA = 6 cmt = 0.3 s
x = cm
5.Hard
mk = 440 N/mA = 10 cmx = 9 cm

A mass on a spring with k = 440 N/m oscillates on a frictionless surface with an amplitude of 10 cm. Find its kinetic energy K when it is 9 cm from equilibrium.

k = 440 N/mA = 10 cmx = 9 cm
K = J
6.Hard
2.7 kgk = 450 N/mA = 9 cm

A 2.7 kg mass on a spring with k = 450 N/m is pulled 9 cm from equilibrium and released. Find its maximum speed vmax.

m = 2.7 kgk = 450 N/mA = 9 cm
vmax = m/s

Answer key

  1. 1. k = 40.28 N/m
  2. 2. T = 0.3753 s
  3. 3. T = 2.975 s
  4. 4. x = −5.937 cm
  5. 5. K = 0.418 J
  6. 6. vmax = 1.162 m/s

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