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
0.5 kgk = ?4 cm

Hanging a 0.5 kg mass on a spring stretches it by 4 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 0.5 kgx = 4 cmg = 9.81 m/s²
k = N/m
2.Easy
1.5 kgk = ?17.5 cm

Hanging a 1.5 kg mass on a spring stretches it by 17.5 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 1.5 kgx = 17.5 cmg = 9.81 m/s²
k = N/m
3.Medium
0.6 kgk = 60 N/mA = 18 cmx = 2 cm

A 0.6 kg mass on a spring with k = 60 N/m oscillates on a frictionless surface with an amplitude of 18 cm. Find its speed v when it is 2 cm from equilibrium.

m = 0.6 kgk = 60 N/mA = 18 cmx = 2 cm
v = m/s
4.Medium
t (s)x (cm)1.3 s

A 3.6 kg mass on a spring with k = 360 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 = 1.3 s (with sign).

m = 3.6 kgk = 360 N/mA = 6 cmt = 1.3 s
x = cm
5.Hard
mk = 420 N/mA = 9 cmx = 1 cm

A mass on a spring with k = 420 N/m oscillates on a frictionless surface with an amplitude of 9 cm. Find its kinetic energy K when it is 1 cm from equilibrium.

k = 420 N/mA = 9 cmx = 1 cm
K = J
6.Hard
3.7 kgk = 470 N/mA = 15 cm

A 3.7 kg mass on a spring with k = 470 N/m is pulled 15 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.7 kgk = 470 N/mA = 15 cm
vmax = m/s

Answer key

  1. 1. k = 122.6 N/m
  2. 2. k = 84.09 N/m
  3. 3. v = 1.789 m/s
  4. 4. x = 5.445 cm
  5. 5. K = 1.68 J
  6. 6. vmax = 1.691 m/s

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