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
2.5 kgk4.5 cm

Hanging a 2.5 kg mass on a spring stretches it by 4.5 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 = 2.5 kgx = 4.5 cmg = 9.81 m/s²
T = s
2.Easy
0.4 kgk = 200 N/m

A 0.4 kg mass on a spring with stiffness 200 N/m oscillates on a frictionless surface. Find the period T.

m = 0.4 kgk = 200 N/m
T = s
3.Medium
t (s)x (cm)0.9 s

A 2.1 kg mass on a spring with k = 180 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 = 0.9 s (with sign).

m = 2.1 kgk = 180 N/mA = 6 cmt = 0.9 s
x = cm
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2.8 s? Use g = 9.81 m/s². Find L.

T = 2.8 sg = 9.81 m/s²
L = m
5.Hard
3.2 kgk = 330 N/mA = 12 cm

A 3.2 kg mass on a spring with k = 330 N/m is pulled 12 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.2 kgk = 330 N/mA = 12 cm
vmax = m/s
6.Hard
3.6 kgk = 210 N/mA = 3 cm

A 3.6 kg mass on a spring with k = 210 N/m is pulled 3 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.6 kgk = 210 N/mA = 3 cm
amax = m/s²

Answer key

  1. 1. T = 0.4256 s
  2. 2. T = 0.281 s
  3. 3. x = −2.762 cm
  4. 4. L = 1.948 m
  5. 5. vmax = 1.219 m/s
  6. 6. amax = 1.75 m/s²

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