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 kgk = ?

A 0.6 kg mass on a spring oscillates with a period of 1.45 s. Find the spring stiffness k.

m = 0.6 kgT = 1.45 s
k = N/m
2.Easy
5 kgk = ?

A 5 kg mass on a spring oscillates with a period of 0.75 s. Find the spring stiffness k.

m = 5 kgT = 0.75 s
k = N/m
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2.4 s? Use g = 9.81 m/s². Find L.

T = 2.4 sg = 9.81 m/s²
L = m
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2.1 s? Use g = 9.81 m/s². Find L.

T = 2.1 sg = 9.81 m/s²
L = m
5.Hard
1.1 kgk = 250 N/mA = 10 cm

A 1.1 kg mass on a spring with k = 250 N/m is pulled 10 cm from equilibrium and released. Find its maximum speed vmax.

m = 1.1 kgk = 250 N/mA = 10 cm
vmax = m/s
6.Hard
mk = 250 N/mA = 15 cmx = 13 cm

A mass on a spring with k = 250 N/m oscillates on a frictionless surface with an amplitude of 15 cm. Find its kinetic energy K when it is 13 cm from equilibrium.

k = 250 N/mA = 15 cmx = 13 cm
K = J

Answer key

  1. 1. k = 11.27 N/m
  2. 2. k = 350.9 N/m
  3. 3. L = 1.431 m
  4. 4. L = 1.096 m
  5. 5. vmax = 1.508 m/s
  6. 6. K = 0.7 J

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