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
1.1 kgk

A 1.1 kg mass on a spring makes 20 complete oscillations in 26 s. Find the frequency f of the oscillation.

m = 1.1 kgN = 20t = 26 s
f = Hz
2.Easy
5 kgk = ?

A 5 kg mass on a spring oscillates with a period of 0.65 s. Find the spring stiffness k.

m = 5 kgT = 0.65 s
k = N/m
3.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
4.Medium
L = ?

How long must a simple pendulum be to have a period of 3 s? Use g = 9.81 m/s². Find L.

T = 3 sg = 9.81 m/s²
L = m
5.Hard
3.9 kgk = 320 N/mA = 5 cm

A 3.9 kg mass on a spring with k = 320 N/m is pulled 5 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.9 kgk = 320 N/mA = 5 cm
amax = m/s²
6.Hard
3.1 kgk = 160 N/mA = 17 cm

A 3.1 kg mass on a spring with k = 160 N/m is pulled 17 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.1 kgk = 160 N/mA = 17 cm
amax = m/s²

Answer key

  1. 1. f = 0.7692 Hz
  2. 2. k = 467.2 N/m
  3. 3. L = 0.2013 m
  4. 4. L = 2.236 m
  5. 5. amax = 4.103 m/s²
  6. 6. amax = 8.774 m/s²

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