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
3.7 kgk = 310 N/m

A 3.7 kg mass on a spring with stiffness 310 N/m oscillates on a frictionless surface. Find the frequency f.

m = 3.7 kgk = 310 N/m
f = Hz
2.Easy
3.6 kgk = 130 N/m

A 3.6 kg mass on a spring with stiffness 130 N/m oscillates on a frictionless surface. Find the frequency f.

m = 3.6 kgk = 130 N/m
f = Hz
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1.2 s? Use g = 9.81 m/s². Find L.

T = 1.2 sg = 9.81 m/s²
L = m
4.Medium
t (s)x (cm)0.9 s

A 3 kg mass on a spring with k = 300 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 = 3 kgk = 300 N/mA = 6 cmt = 0.9 s
x = cm
5.Hard
mk = 500 N/mA = 12 cmx = 7 cm

A mass on a spring with k = 500 N/m oscillates on a frictionless surface with an amplitude of 12 cm. Find its kinetic energy K when it is 7 cm from equilibrium.

k = 500 N/mA = 12 cmx = 7 cm
K = J
6.Hard
4 kgk = 290 N/mA = 17 cm

A 4 kg mass on a spring with k = 290 N/m is pulled 17 cm from equilibrium and released. Find its maximum acceleration amax.

m = 4 kgk = 290 N/mA = 17 cm
amax = m/s²

Answer key

  1. 1. f = 1.457 Hz
  2. 2. f = 0.9564 Hz
  3. 3. L = 0.3578 m
  4. 4. x = −5.467 cm
  5. 5. K = 2.375 J
  6. 6. amax = 12.33 m/s²

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