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
3.6 kgk

A 3.6 kg mass on a spring makes 20 complete oscillations in 19 s. Find the frequency f of the oscillation.

m = 3.6 kgN = 20t = 19 s
f = Hz
2.Easy
2 kgk = ?14.5 cm

Hanging a 2 kg mass on a spring stretches it by 14.5 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 2 kgx = 14.5 cmg = 9.81 m/s²
k = N/m
3.Medium
L = 1.5 m

A simple pendulum has a length of 1.5 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.5 mg = 9.81 m/s²
T = s
4.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
5.Hard
2.2 kgk = 240 N/mA = 13 cm

A 2.2 kg mass on a spring with k = 240 N/m is pulled 13 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 2.2 kgk = 240 N/mA = 13 cm
E = J
6.Hard
3.2 kgk = 380 N/mA = 13 cm

A 3.2 kg mass on a spring with k = 380 N/m is pulled 13 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.2 kgk = 380 N/mA = 13 cm
vmax = m/s

Answer key

  1. 1. f = 1.053 Hz
  2. 2. k = 135.3 N/m
  3. 3. T = 2.457 s
  4. 4. L = 0.7181 m
  5. 5. E = 2.028 J
  6. 6. vmax = 1.417 m/s

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