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
2.2 kgk14 cm

Hanging a 2.2 kg mass on a spring stretches it by 14 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 = 2.2 kgx = 14 cmg = 9.81 m/s²
T = s
2.Easy
2.2 kgk = ?16.5 cm

Hanging a 2.2 kg mass on a spring stretches it by 16.5 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 2.2 kgx = 16.5 cmg = 9.81 m/s²
k = N/m
3.Medium
L = 1.8 mT = 4.38 s

An astronaut on another planet finds that a simple pendulum 1.8 m long has a period of 4.38 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.8 mT = 4.38 s
g = m/s²
4.Medium
t (s)x (cm)0.15 s

A 4 kg mass on a spring with k = 200 N/m is pulled 11 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 0.15 s (with sign).

m = 4 kgk = 200 N/mA = 11 cmt = 0.15 s
v = m/s
5.Hard
1.3 kgk = 390 N/mA = 2 cm

A 1.3 kg mass on a spring with k = 390 N/m is pulled 2 cm from equilibrium and released. Find its maximum acceleration amax.

m = 1.3 kgk = 390 N/mA = 2 cm
amax = m/s²
6.Hard
0.4 kgk = 460 N/mA = 12 cm

A 0.4 kg mass on a spring with k = 460 N/m is pulled 12 cm from equilibrium and released. Find its maximum speed vmax.

m = 0.4 kgk = 460 N/mA = 12 cm
vmax = m/s

Answer key

  1. 1. T = 0.7506 s
  2. 2. k = 130.8 N/m
  3. 3. g = 3.704 m/s²
  4. 4. v = −0.6788 m/s
  5. 5. amax = 6 m/s²
  6. 6. vmax = 4.069 m/s

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