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
0.6 kgk = 170 N/m

A 0.6 kg mass on a spring with stiffness 170 N/m oscillates on a frictionless surface. Find the frequency f.

m = 0.6 kgk = 170 N/m
f = Hz
2.Easy
3.8 kgk = ?

A 3.8 kg mass on a spring makes 25 complete oscillations in 38 s. Find the spring stiffness k.

m = 3.8 kgN = 25t = 38 s
k = N/m
3.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
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1 s? Use g = 9.81 m/s². Find L.

T = 1 sg = 9.81 m/s²
L = m
5.Hard
3.3 kgk = 50 N/mA = 3 cm

A 3.3 kg mass on a spring with k = 50 N/m is pulled 3 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.3 kgk = 50 N/mA = 3 cm
amax = m/s²
6.Hard
0.6 kgk = 130 N/mA = 5 cm

A 0.6 kg mass on a spring with k = 130 N/m is pulled 5 cm from equilibrium and released. Find its maximum acceleration amax.

m = 0.6 kgk = 130 N/mA = 5 cm
amax = m/s²

Answer key

  1. 1. f = 2.679 Hz
  2. 2. k = 64.93 N/m
  3. 3. T = 3.108 s
  4. 4. L = 0.2485 m
  5. 5. amax = 0.4545 m/s²
  6. 6. amax = 10.83 m/s²

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