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 kgk12 cm

Hanging a 0.3 kg mass on a spring stretches it by 12 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 = 12 cmg = 9.81 m/s²
T = s
2.Easy
4.2 kgk = 370 N/m

A 4.2 kg mass on a spring with stiffness 370 N/m oscillates on a frictionless surface. Find the frequency f.

m = 4.2 kgk = 370 N/m
f = Hz
3.Medium
t (s)x (cm)1.15 s

A 0.8 kg mass on a spring with k = 220 N/m is pulled 12 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 1.15 s (with sign).

m = 0.8 kgk = 220 N/mA = 12 cmt = 1.15 s
x = cm
4.Medium
L = 0.5 m

A simple pendulum has a length of 0.5 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.5 mg = 9.81 m/s²
T = s
5.Hard
3.2 kgk = 370 N/mA = 14 cm

A 3.2 kg mass on a spring with k = 370 N/m is pulled 14 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.2 kgk = 370 N/mA = 14 cm
vmax = m/s
6.Hard
4 kgk = 2000 N/m500 m/s

A 15 g bullet moving at 500 m/s hits and stays in a 4 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 2000 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 15 gv = 500 m/sM = 4 kgk = 2000 N/m
A = cm

Answer key

  1. 1. T = 0.6949 s
  2. 2. f = 1.494 Hz
  3. 3. x = 11.71 cm
  4. 4. T = 1.419 s
  5. 5. vmax = 1.505 m/s
  6. 6. A = 8.37 cm

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