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
2.5 kgk = ?21 cm

Hanging a 2.5 kg mass on a spring stretches it by 21 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 2.5 kgx = 21 cmg = 9.81 m/s²
k = N/m
2.Easy
1.1 kgk = 390 N/m

A 1.1 kg mass on a spring with stiffness 390 N/m oscillates on a frictionless surface. Find the frequency f.

m = 1.1 kgk = 390 N/m
f = Hz
3.Medium
t (s)x (cm)0.55 s

A 3.9 kg mass on a spring with k = 320 N/m is pulled 14 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.55 s (with sign).

m = 3.9 kgk = 320 N/mA = 14 cmt = 0.55 s
x = cm
4.Medium
1.9 kgk = 450 N/mA = 8 cmx = 6 cm

A 1.9 kg mass on a spring with k = 450 N/m oscillates on a frictionless surface with an amplitude of 8 cm. Find its speed v when it is 6 cm from equilibrium.

m = 1.9 kgk = 450 N/mA = 8 cmx = 6 cm
v = m/s
5.Hard
mk = 180 N/mA = 14 cmx = 8 cm

A mass on a spring with k = 180 N/m oscillates on a frictionless surface with an amplitude of 14 cm. Find its kinetic energy K when it is 8 cm from equilibrium.

k = 180 N/mA = 14 cmx = 8 cm
K = J
6.Hard
1.8 kgk = 340 N/mA = 20 cm

A 1.8 kg mass on a spring with k = 340 N/m is pulled 20 cm from equilibrium and released. Find its maximum speed vmax.

m = 1.8 kgk = 340 N/mA = 20 cm
vmax = m/s

Answer key

  1. 1. k = 116.8 N/m
  2. 2. f = 2.997 Hz
  3. 3. x = 3.729 cm
  4. 4. v = 0.8143 m/s
  5. 5. K = 1.188 J
  6. 6. vmax = 2.749 m/s

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