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
0.8 kgk24.5 cm

Hanging a 0.8 kg mass on a spring stretches it by 24.5 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 = 0.8 kgx = 24.5 cmg = 9.81 m/s²
T = s
2.Easy
3.6 kgk = 250 N/m

A 3.6 kg mass on a spring with stiffness 250 N/m oscillates on a frictionless surface. Find the period T.

m = 3.6 kgk = 250 N/m
T = s
3.Medium
0.4 kgk = 460 N/mA = 17 cmx = 6 cm

A 0.4 kg mass on a spring with k = 460 N/m oscillates on a frictionless surface with an amplitude of 17 cm. Find its speed v when it is 6 cm from equilibrium.

m = 0.4 kgk = 460 N/mA = 17 cmx = 6 cm
v = m/s
4.Medium
t (s)x (cm)0.95 s

A 1.7 kg mass on a spring with k = 20 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 = 0.95 s (with sign).

m = 1.7 kgk = 20 N/mA = 3 cmt = 0.95 s
x = cm
5.Hard
3.3 kgk = 380 N/mA = 3 cm

A 3.3 kg mass on a spring with k = 380 N/m is pulled 3 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.3 kgk = 380 N/mA = 3 cm
amax = m/s²
6.Hard
0.5 kgk = 180 N/mA = 17 cm

A 0.5 kg mass on a spring with k = 180 N/m is pulled 17 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 0.5 kgk = 180 N/mA = 17 cm
E = J

Answer key

  1. 1. T = 0.993 s
  2. 2. T = 0.754 s
  3. 3. v = 5.394 m/s
  4. 4. x = −2.98 cm
  5. 5. amax = 3.455 m/s²
  6. 6. E = 2.601 J

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