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
0.4 kgk

A 0.4 kg mass on a spring makes 30 complete oscillations in 51 s. Find the frequency f of the oscillation.

m = 0.4 kgN = 30t = 51 s
f = Hz
2.Easy
3.6 kgk = 220 N/m

A 3.6 kg mass on a spring with stiffness 220 N/m oscillates on a frictionless surface. Find the period T.

m = 3.6 kgk = 220 N/m
T = s
3.Medium
L = 2.6 m

A simple pendulum has a length of 2.6 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.6 mg = 9.81 m/s²
T = s
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.8 s? Use g = 9.81 m/s². Find L.

T = 1.8 sg = 9.81 m/s²
L = m
5.Hard
0.5 kgk = 450 N/mA = 4 cm

A 0.5 kg mass on a spring with k = 450 N/m is pulled 4 cm from equilibrium and released. Find its maximum acceleration amax.

m = 0.5 kgk = 450 N/mA = 4 cm
amax = m/s²
6.Hard
1.3 kgk = 350 N/mA = 20 cm

A 1.3 kg mass on a spring with k = 350 N/m is pulled 20 cm from equilibrium and released. Find its maximum speed vmax.

m = 1.3 kgk = 350 N/mA = 20 cm
vmax = m/s

Answer key

  1. 1. f = 0.5882 Hz
  2. 2. T = 0.8037 s
  3. 3. T = 3.235 s
  4. 4. L = 0.8051 m
  5. 5. amax = 36 m/s²
  6. 6. vmax = 3.282 m/s

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