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
0.9 kgk = ?

A 0.9 kg mass on a spring oscillates with a period of 1.75 s. Find the spring stiffness k.

m = 0.9 kgT = 1.75 s
k = N/m
2.Easy
2.6 kgk17 cm

Hanging a 2.6 kg mass on a spring stretches it by 17 cm. Use g = 9.81 m/s². The mass is then pulled down a little and released. Find the period T of its oscillation.

m = 2.6 kgx = 17 cmg = 9.81 m/s²
T = s
3.Medium
t (s)x (cm)1.15 s

A 0.2 kg mass on a spring with k = 270 N/m is pulled 6 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 1.15 s (with sign).

m = 0.2 kgk = 270 N/mA = 6 cmt = 1.15 s
x = cm
4.Medium
L = 1.3 mT = 3.71 s

An astronaut on another planet finds that a simple pendulum 1.3 m long has a period of 3.71 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.3 mT = 3.71 s
g = m/s²
5.Hard
3.5 kgk = 190 N/mA = 18 cm

A 3.5 kg mass on a spring with k = 190 N/m is pulled 18 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 3.5 kgk = 190 N/mA = 18 cm
E = J
6.Hard
3.1 kgk = 390 N/mA = 20 cm

A 3.1 kg mass on a spring with k = 390 N/m is pulled 20 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.1 kgk = 390 N/mA = 20 cm
vmax = m/s

Answer key

  1. 1. k = 11.6 N/m
  2. 2. T = 0.8271 s
  3. 3. x = −0.9429 cm
  4. 4. g = 3.729 m/s²
  5. 5. E = 3.078 J
  6. 6. vmax = 2.243 m/s

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