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
0.3 kgk14 cm

Hanging a 0.3 kg mass on a spring stretches it by 14 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 = 0.3 kgx = 14 cmg = 9.81 m/s²
T = s
2.Easy
2.1 kgk = ?13 cm

Hanging a 2.1 kg mass on a spring stretches it by 13 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 2.1 kgx = 13 cmg = 9.81 m/s²
k = N/m
3.Medium
L = 1.5 mT = 2.58 s

An astronaut on another planet finds that a simple pendulum 1.5 m long has a period of 2.58 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.5 mT = 2.58 s
g = m/s²
4.Medium
t (s)x (cm)1.5 s

A 0.8 kg mass on a spring with k = 210 N/m is pulled 14 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 1.5 s (with sign).

m = 0.8 kgk = 210 N/mA = 14 cmt = 1.5 s
x = cm
5.Hard
1.7 kgk = 40 N/mA = 7 cm

A 1.7 kg mass on a spring with k = 40 N/m is pulled 7 cm from equilibrium and released. Find its maximum speed vmax.

m = 1.7 kgk = 40 N/mA = 7 cm
vmax = m/s
6.Hard
mk = 70 N/mA = 5 cmx = 2 cm

A mass on a spring with k = 70 N/m oscillates on a frictionless surface with an amplitude of 5 cm. Find its kinetic energy K when it is 2 cm from equilibrium.

k = 70 N/mA = 5 cmx = 2 cm
K = J

Answer key

  1. 1. T = 0.7506 s
  2. 2. k = 158.5 N/m
  3. 3. g = 8.896 m/s²
  4. 4. x = 9.449 cm
  5. 5. vmax = 0.3395 m/s
  6. 6. K = 0.0735 J

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