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
1.5 kgk = 290 N/m

A 1.5 kg mass on a spring with stiffness 290 N/m oscillates on a frictionless surface. Find the period T.

m = 1.5 kgk = 290 N/m
T = s
2.Easy
1.5 kgk = 380 N/m

A 1.5 kg mass on a spring with stiffness 380 N/m oscillates on a frictionless surface. Find the frequency f.

m = 1.5 kgk = 380 N/m
f = Hz
3.Medium
L = 1 m

A simple pendulum has a length of 1 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1 mg = 9.81 m/s²
T = s
4.Medium
t (s)x (cm)0.4 s

A 3.8 kg mass on a spring with k = 30 N/m is pulled 15 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.4 s (with sign).

m = 3.8 kgk = 30 N/mA = 15 cmt = 0.4 s
x = cm
5.Hard
mk = 150 N/mA = 10 cmx = 5 cm

A mass on a spring with k = 150 N/m oscillates on a frictionless surface with an amplitude of 10 cm. Find the energy U stored in the spring when the mass is 5 cm from equilibrium.

k = 150 N/mA = 10 cmx = 5 cm
U = J
6.Hard
0.5 kgk = 480 N/m

A 0.5 kg mass is attached to the lower end of an unstretched vertical spring with k = 480 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 0.5 kgk = 480 N/mg = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. T = 0.4519 s
  2. 2. f = 2.533 Hz
  3. 3. T = 2.006 s
  4. 4. x = 6.482 cm
  5. 5. U = 0.1875 J
  6. 6. vmax = 0.3166 m/s

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