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
2.8 kgk = ?

A 2.8 kg mass on a spring oscillates with a period of 1.1 s. Find the spring stiffness k.

m = 2.8 kgT = 1.1 s
k = N/m
2.Easy
3.7 kgk = ?

A 3.7 kg mass on a spring makes 40 complete oscillations in 31 s. Find the spring stiffness k.

m = 3.7 kgN = 40t = 31 s
k = N/m
3.Medium
t (s)x (cm)1 s

A 0.5 kg mass on a spring with k = 190 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 s (with sign).

m = 0.5 kgk = 190 N/mA = 11 cmt = 1 s
x = cm
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.6 s? Use g = 9.81 m/s². Find L.

T = 1.6 sg = 9.81 m/s²
L = m
5.Hard
1.7 kgk = 310 N/m

A 1.7 kg mass is attached to the lower end of an unstretched vertical spring with k = 310 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 1.7 kgk = 310 N/mg = 9.81 m/s²
vmax = m/s
6.Hard
mk = 390 N/mA = 8 cmx = 2 cm

A mass on a spring with k = 390 N/m oscillates on a frictionless surface with an amplitude of 8 cm. Find its kinetic energy K when it is 2 cm from equilibrium.

k = 390 N/mA = 8 cmx = 2 cm
K = J

Answer key

  1. 1. k = 91.36 N/m
  2. 2. k = 243.2 N/m
  3. 3. x = 8.796 cm
  4. 4. L = 0.6361 m
  5. 5. vmax = 0.7265 m/s
  6. 6. K = 1.17 J

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