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
2.6 kgk13.5 cm

Hanging a 2.6 kg mass on a spring stretches it by 13.5 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 = 2.6 kgx = 13.5 cmg = 9.81 m/s²
T = s
2.Easy
3.8 kgk = 180 N/m

A 3.8 kg mass on a spring with stiffness 180 N/m oscillates on a frictionless surface. Find the period T.

m = 3.8 kgk = 180 N/m
T = s
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2.4 s? Use g = 9.81 m/s². Find L.

T = 2.4 sg = 9.81 m/s²
L = m
4.Medium
L = 2.4 m

A simple pendulum has a length of 2.4 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.4 mg = 9.81 m/s²
T = s
5.Hard
3.5 kgk = 1200 N/m350 m/s

A 15 g bullet moving at 350 m/s hits and stays in a 3.5 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1200 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 15 gv = 350 m/sM = 3.5 kgk = 1200 N/m
A = cm
6.Hard
mk = 300 N/mA = 8 cmx = 5 cm

A mass on a spring with k = 300 N/m oscillates on a frictionless surface with an amplitude of 8 cm. Find its kinetic energy K when it is 5 cm from equilibrium.

k = 300 N/mA = 8 cmx = 5 cm
K = J

Answer key

  1. 1. T = 0.7371 s
  2. 2. T = 0.9129 s
  3. 3. L = 1.431 m
  4. 4. T = 3.108 s
  5. 5. A = 8.084 cm
  6. 6. K = 0.585 J

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