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
2.9 kgk2 cm

Hanging a 2.9 kg mass on a spring stretches it by 2 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 = 2.9 kgx = 2 cmg = 9.81 m/s²
T = s
2.Easy
1.7 kgk = 40 N/m

A 1.7 kg mass on a spring with stiffness 40 N/m oscillates on a frictionless surface. Find the period T.

m = 1.7 kgk = 40 N/m
T = s
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2.8 s? Use g = 9.81 m/s². Find L.

T = 2.8 sg = 9.81 m/s²
L = m
4.Medium
3.5 kgk = 440 N/mA = 19 cmx = 3 cm

A 3.5 kg mass on a spring with k = 440 N/m oscillates on a frictionless surface with an amplitude of 19 cm. Find its speed v when it is 3 cm from equilibrium.

m = 3.5 kgk = 440 N/mA = 19 cmx = 3 cm
v = m/s
5.Hard
mk = 270 N/mA = 14 cmx = 8 cm

A mass on a spring with k = 270 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 = 270 N/mA = 14 cmx = 8 cm
K = J
6.Hard
1.9 kgk = 390 N/mA = 19 cm

A 1.9 kg mass on a spring with k = 390 N/m is pulled 19 cm from equilibrium and released. Find its maximum speed vmax.

m = 1.9 kgk = 390 N/mA = 19 cm
vmax = m/s

Answer key

  1. 1. T = 0.2837 s
  2. 2. T = 1.295 s
  3. 3. L = 1.948 m
  4. 4. v = 2.104 m/s
  5. 5. K = 1.782 J
  6. 6. vmax = 2.722 m/s

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