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
1.8 kgk = ?11.5 cm

Hanging a 1.8 kg mass on a spring stretches it by 11.5 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 1.8 kgx = 11.5 cmg = 9.81 m/s²
k = N/m
2.Easy
4.8 kgk = 140 N/m

A 4.8 kg mass on a spring with stiffness 140 N/m oscillates on a frictionless surface. Find the period T.

m = 4.8 kgk = 140 N/m
T = s
3.Medium
L = 0.4 m

A simple pendulum has a length of 0.4 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.4 mg = 9.81 m/s²
T = s
4.Medium
t (s)x (cm)0.15 s

A 3.6 kg mass on a spring with k = 300 N/m is pulled 8 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.15 s (with sign).

m = 3.6 kgk = 300 N/mA = 8 cmt = 0.15 s
x = cm
5.Hard
0.3 kgk = 230 N/mA = 19 cm

A 0.3 kg mass on a spring with k = 230 N/m is pulled 19 cm from equilibrium and released. Find its maximum acceleration amax.

m = 0.3 kgk = 230 N/mA = 19 cm
amax = m/s²
6.Hard
mk = 320 N/mA = 17 cmx = 14 cm

A mass on a spring with k = 320 N/m oscillates on a frictionless surface with an amplitude of 17 cm. Find the energy U stored in the spring when the mass is 14 cm from equilibrium.

k = 320 N/mA = 17 cmx = 14 cm
U = J

Answer key

  1. 1. k = 153.5 N/m
  2. 2. T = 1.163 s
  3. 3. T = 1.269 s
  4. 4. x = 1.601 cm
  5. 5. amax = 145.7 m/s²
  6. 6. U = 3.136 J

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