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
2.9 kgk = ?12.5 cm

Hanging a 2.9 kg mass on a spring stretches it by 12.5 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 2.9 kgx = 12.5 cmg = 9.81 m/s²
k = N/m
2.Easy
3.5 kgk = ?

A 3.5 kg mass on a spring oscillates with a period of 0.65 s. Find the spring stiffness k.

m = 3.5 kgT = 0.65 s
k = N/m
3.Medium
L = 1.8 m

A simple pendulum has a length of 1.8 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.8 mg = 9.81 m/s²
T = s
4.Medium
t (s)x (cm)1.3 s

A 1.2 kg mass on a spring with k = 330 N/m is pulled 8 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 1.3 s (with sign).

m = 1.2 kgk = 330 N/mA = 8 cmt = 1.3 s
v = m/s
5.Hard
mk = 440 N/mA = 6 cmx = 4 cm

A mass on a spring with k = 440 N/m oscillates on a frictionless surface with an amplitude of 6 cm. Find the energy U stored in the spring when the mass is 4 cm from equilibrium.

k = 440 N/mA = 6 cmx = 4 cm
U = J
6.Hard
1.7 kgk = 370 N/mA = 12 cm

A 1.7 kg mass on a spring with k = 370 N/m is pulled 12 cm from equilibrium and released. Find its maximum acceleration amax.

m = 1.7 kgk = 370 N/mA = 12 cm
amax = m/s²

Answer key

  1. 1. k = 227.6 N/m
  2. 2. k = 327 N/m
  3. 3. T = 2.691 s
  4. 4. v = −0.5568 m/s
  5. 5. U = 0.352 J
  6. 6. amax = 26.12 m/s²

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