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
2.2 kgk = 70 N/m

A 2.2 kg mass on a spring with stiffness 70 N/m oscillates on a frictionless surface. Find the period T.

m = 2.2 kgk = 70 N/m
T = s
2.Easy
0.7 kgk = 100 N/m

A 0.7 kg mass on a spring with stiffness 100 N/m oscillates on a frictionless surface. Find the period T.

m = 0.7 kgk = 100 N/m
T = s
3.Medium
t (s)x (cm)0.35 s

A 2.1 kg mass on a spring with k = 130 N/m is pulled 10 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.35 s (with sign).

m = 2.1 kgk = 130 N/mA = 10 cmt = 0.35 s
x = cm
4.Medium
L = 1.9 m

A simple pendulum has a length of 1.9 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.9 mg = 9.81 m/s²
T = s
5.Hard
mk = 350 N/mA = 13 cmx = 4 cm

A mass on a spring with k = 350 N/m oscillates on a frictionless surface with an amplitude of 13 cm. Find the energy U stored in the spring when the mass is 4 cm from equilibrium.

k = 350 N/mA = 13 cmx = 4 cm
U = J
6.Hard
3 kgk = 1400 N/m100 m/s

A 20 g bullet moving at 100 m/s hits and stays in a 3 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1400 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 20 gv = 100 m/sM = 3 kgk = 1400 N/m
A = cm

Answer key

  1. 1. T = 1.114 s
  2. 2. T = 0.5257 s
  3. 3. x = −9.257 cm
  4. 4. T = 2.765 s
  5. 5. U = 0.28 J
  6. 6. A = 3.076 cm

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