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
4.2 kgk = ?

A 4.2 kg mass on a spring oscillates with a period of 2.25 s. Find the spring stiffness k.

m = 4.2 kgT = 2.25 s
k = N/m
2.Easy
1.5 kgk = 90 N/m

A 1.5 kg mass on a spring with stiffness 90 N/m oscillates on a frictionless surface. Find the frequency f.

m = 1.5 kgk = 90 N/m
f = Hz
3.Medium
t (s)x (cm)1.15 s

A 1 kg mass on a spring with k = 250 N/m is pulled 3 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 = 1 kgk = 250 N/mA = 3 cmt = 1.15 s
x = cm
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
mk = 320 N/mA = 7 cmx = 4 cm

A mass on a spring with k = 320 N/m oscillates on a frictionless surface with an amplitude of 7 cm. Find the energy U stored in the spring when the mass is 4 cm from equilibrium.

k = 320 N/mA = 7 cmx = 4 cm
U = J
6.Hard
2.7 kgk = 320 N/mA = 18 cm

A 2.7 kg mass on a spring with k = 320 N/m is pulled 18 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 2.7 kgk = 320 N/mA = 18 cm
E = J

Answer key

  1. 1. k = 32.75 N/m
  2. 2. f = 1.233 Hz
  3. 3. x = 2.358 cm
  4. 4. T = 3.108 s
  5. 5. U = 0.256 J
  6. 6. E = 5.184 J

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