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
0.6 kgk17 cm

Hanging a 0.6 kg mass on a spring stretches it by 17 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 = 0.6 kgx = 17 cmg = 9.81 m/s²
T = s
2.Easy
2.8 kgk = 350 N/m

A 2.8 kg mass on a spring with stiffness 350 N/m oscillates on a frictionless surface. Find the period T.

m = 2.8 kgk = 350 N/m
T = s
3.Medium
2.6 kgk = 40 N/mA = 18 cmx = 7 cm

A 2.6 kg mass on a spring with k = 40 N/m oscillates on a frictionless surface with an amplitude of 18 cm. Find its speed v when it is 7 cm from equilibrium.

m = 2.6 kgk = 40 N/mA = 18 cmx = 7 cm
v = m/s
4.Medium
t (s)x (cm)1.2 s

A 1.8 kg mass on a spring with k = 270 N/m is pulled 11 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 1.2 s (with sign).

m = 1.8 kgk = 270 N/mA = 11 cmt = 1.2 s
x = cm
5.Hard
3.5 kgk = 200 N/mA = 4 cm

A 3.5 kg mass on a spring with k = 200 N/m is pulled 4 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.5 kgk = 200 N/mA = 4 cm
amax = m/s²
6.Hard
3 kgk = 130 N/m

A 3 kg mass is attached to the lower end of an unstretched vertical spring with k = 130 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 3 kgk = 130 N/mg = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. T = 0.8271 s
  2. 2. T = 0.562 s
  3. 3. v = 0.6504 m/s
  4. 4. x = −5.841 cm
  5. 5. amax = 2.286 m/s²
  6. 6. vmax = 1.49 m/s

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