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
0.6 kgk = ?

A 0.6 kg mass on a spring oscillates with a period of 1.35 s. Find the spring stiffness k.

m = 0.6 kgT = 1.35 s
k = N/m
2.Easy
0.6 kgk = ?

A 0.6 kg mass on a spring oscillates with a period of 1.55 s. Find the spring stiffness k.

m = 0.6 kgT = 1.55 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
L = 2.2 m

A simple pendulum has a length of 2.2 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.2 mg = 9.81 m/s²
T = s
5.Hard
mk = 460 N/mA = 19 cmx = 6 cm

A mass on a spring with k = 460 N/m oscillates on a frictionless surface with an amplitude of 19 cm. Find the energy U stored in the spring when the mass is 6 cm from equilibrium.

k = 460 N/mA = 19 cmx = 6 cm
U = J
6.Hard
2 kgk = 900 N/m350 m/s

A 5 g bullet moving at 350 m/s hits and stays in a 2 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 900 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 5 gv = 350 m/sM = 2 kgk = 900 N/m
A = cm

Answer key

  1. 1. k = 13 N/m
  2. 2. k = 9.859 N/m
  3. 3. T = 2.691 s
  4. 4. T = 2.975 s
  5. 5. U = 0.828 J
  6. 6. A = 4.12 cm

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