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
3.1 kgk = 170 N/m

A 3.1 kg mass on a spring with stiffness 170 N/m oscillates on a frictionless surface. Find the period T.

m = 3.1 kgk = 170 N/m
T = s
2.Easy
4.6 kgk = 310 N/m

A 4.6 kg mass on a spring with stiffness 310 N/m oscillates on a frictionless surface. Find the frequency f.

m = 4.6 kgk = 310 N/m
f = Hz
3.Medium
L = 2.5 m

A simple pendulum has a length of 2.5 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.5 mg = 9.81 m/s²
T = s
4.Medium
t (s)x (cm)0.85 s

A 2.1 kg mass on a spring with k = 140 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 = 0.85 s (with sign).

m = 2.1 kgk = 140 N/mA = 3 cmt = 0.85 s
x = cm
5.Hard
0.6 kgk = 70 N/mA = 13 cm

A 0.6 kg mass on a spring with k = 70 N/m is pulled 13 cm from equilibrium and released. Find its maximum acceleration amax.

m = 0.6 kgk = 70 N/mA = 13 cm
amax = m/s²
6.Hard
mk = 270 N/mA = 15 cmx = 14 cm

A mass on a spring with k = 270 N/m oscillates on a frictionless surface with an amplitude of 15 cm. Find its kinetic energy K when it is 14 cm from equilibrium.

k = 270 N/mA = 15 cmx = 14 cm
K = J

Answer key

  1. 1. T = 0.8485 s
  2. 2. f = 1.307 Hz
  3. 3. T = 3.172 s
  4. 4. x = 2.375 cm
  5. 5. amax = 15.17 m/s²
  6. 6. K = 0.3915 J

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