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
4.1 kgk = 400 N/m

A 4.1 kg mass on a spring with stiffness 400 N/m oscillates on a frictionless surface. Find the frequency f.

m = 4.1 kgk = 400 N/m
f = Hz
2.Easy
2.1 kgk = ?

A 2.1 kg mass on a spring oscillates with a period of 2.15 s. Find the spring stiffness k.

m = 2.1 kgT = 2.15 s
k = N/m
3.Medium
L = ?

How long must a simple pendulum be to have a period of 0.8 s? Use g = 9.81 m/s². Find L.

T = 0.8 sg = 9.81 m/s²
L = m
4.Medium
L = 1.6 m

A simple pendulum has a length of 1.6 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.6 mg = 9.81 m/s²
T = s
5.Hard
0.2 kgk = 340 N/mA = 8 cm

A 0.2 kg mass on a spring with k = 340 N/m is pulled 8 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 0.2 kgk = 340 N/mA = 8 cm
E = J
6.Hard
mk = 110 N/mA = 11 cmx = 8 cm

A mass on a spring with k = 110 N/m oscillates on a frictionless surface with an amplitude of 11 cm. Find the energy U stored in the spring when the mass is 8 cm from equilibrium.

k = 110 N/mA = 11 cmx = 8 cm
U = J

Answer key

  1. 1. f = 1.572 Hz
  2. 2. k = 17.94 N/m
  3. 3. L = 0.159 m
  4. 4. T = 2.537 s
  5. 5. E = 1.088 J
  6. 6. U = 0.352 J

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