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
3.8 kgk = ?

A 3.8 kg mass on a spring makes 25 complete oscillations in 34 s. Find the spring stiffness k.

m = 3.8 kgN = 25t = 34 s
k = N/m
2.Easy
3.4 kgk

A 3.4 kg mass on a spring makes 30 complete oscillations in 9 s. Find the frequency f of the oscillation.

m = 3.4 kgN = 30t = 9 s
f = Hz
3.Medium
L = 1.1 m

A simple pendulum has a length of 1.1 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.1 mg = 9.81 m/s²
T = s
4.Medium
t (s)x (cm)1.05 s

A 0.5 kg mass on a spring with k = 80 N/m is pulled 14 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 1.05 s (with sign).

m = 0.5 kgk = 80 N/mA = 14 cmt = 1.05 s
v = m/s
5.Hard
2.4 kgk = 470 N/mA = 9 cm

A 2.4 kg mass on a spring with k = 470 N/m is pulled 9 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 2.4 kgk = 470 N/mA = 9 cm
E = J
6.Hard
0.6 kgk = 210 N/mA = 8 cm

A 0.6 kg mass on a spring with k = 210 N/m is pulled 8 cm from equilibrium and released. Find its maximum acceleration amax.

m = 0.6 kgk = 210 N/mA = 8 cm
amax = m/s²

Answer key

  1. 1. k = 81.11 N/m
  2. 2. f = 3.333 Hz
  3. 3. T = 2.104 s
  4. 4. v = −1.161 m/s
  5. 5. E = 1.903 J
  6. 6. amax = 28 m/s²

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