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
3.9 kgk

A 3.9 kg mass on a spring makes 20 complete oscillations in 25 s. Find the frequency f of the oscillation.

m = 3.9 kgN = 20t = 25 s
f = Hz
2.Easy
2.4 kgk = ?13.5 cm

Hanging a 2.4 kg mass on a spring stretches it by 13.5 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 2.4 kgx = 13.5 cmg = 9.81 m/s²
k = N/m
3.Medium
t (s)x (cm)0.9 s

A 0.5 kg mass on a spring with k = 20 N/m is pulled 3 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.9 s (with sign).

m = 0.5 kgk = 20 N/mA = 3 cmt = 0.9 s
x = cm
4.Medium
L = 1.8 mT = 4.37 s

An astronaut on another planet finds that a simple pendulum 1.8 m long has a period of 4.37 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.8 mT = 4.37 s
g = m/s²
5.Hard
3.2 kgk = 290 N/mA = 10 cm

A 3.2 kg mass on a spring with k = 290 N/m is pulled 10 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.2 kgk = 290 N/mA = 10 cm
vmax = m/s
6.Hard
2.4 kgk = 190 N/mA = 4 cm

A 2.4 kg mass on a spring with k = 190 N/m is pulled 4 cm from equilibrium and released. Find its maximum acceleration amax.

m = 2.4 kgk = 190 N/mA = 4 cm
amax = m/s²

Answer key

  1. 1. f = 0.8 Hz
  2. 2. k = 174.4 N/m
  3. 3. x = 2.491 cm
  4. 4. g = 3.721 m/s²
  5. 5. vmax = 0.952 m/s
  6. 6. amax = 3.167 m/s²

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