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
0.5 kgk = 100 N/m

A 0.5 kg mass on a spring with stiffness 100 N/m oscillates on a frictionless surface. Find the period T.

m = 0.5 kgk = 100 N/m
T = s
2.Easy
1 kgk

A 1 kg mass on a spring makes 10 complete oscillations in 8 s. Find the frequency f of the oscillation.

m = 1 kgN = 10t = 8 s
f = Hz
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1.7 s? Use g = 9.81 m/s². Find L.

T = 1.7 sg = 9.81 m/s²
L = m
4.Medium
L = ?

How long must a simple pendulum be to have a period of 0.9 s? Use g = 9.81 m/s². Find L.

T = 0.9 sg = 9.81 m/s²
L = m
5.Hard
mk = 490 N/mA = 13 cmx = 7 cm

A mass on a spring with k = 490 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 7 cm from equilibrium.

k = 490 N/mA = 13 cmx = 7 cm
U = J
6.Hard
2.6 kgk = 30 N/mA = 5 cm

A 2.6 kg mass on a spring with k = 30 N/m is pulled 5 cm from equilibrium and released. Find its maximum acceleration amax.

m = 2.6 kgk = 30 N/mA = 5 cm
amax = m/s²

Answer key

  1. 1. T = 0.4443 s
  2. 2. f = 1.25 Hz
  3. 3. L = 0.7181 m
  4. 4. L = 0.2013 m
  5. 5. U = 1.201 J
  6. 6. amax = 0.5769 m/s²

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