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
1.9 kgk = 180 N/m

A 1.9 kg mass on a spring with stiffness 180 N/m oscillates on a frictionless surface. Find the period T.

m = 1.9 kgk = 180 N/m
T = s
2.Easy
0.1 kgk = ?8 cm

Hanging a 0.1 kg mass on a spring stretches it by 8 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 0.1 kgx = 8 cmg = 9.81 m/s²
k = N/m
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2.2 s? Use g = 9.81 m/s². Find L.

T = 2.2 sg = 9.81 m/s²
L = m
4.Medium
2 kgk = 130 N/mA = 17 cmx = 2 cm

A 2 kg mass on a spring with k = 130 N/m oscillates on a frictionless surface with an amplitude of 17 cm. Find its speed v when it is 2 cm from equilibrium.

m = 2 kgk = 130 N/mA = 17 cmx = 2 cm
v = m/s
5.Hard
2.8 kgk = 100 N/mA = 15 cm

A 2.8 kg mass on a spring with k = 100 N/m is pulled 15 cm from equilibrium and released. Find its maximum speed vmax.

m = 2.8 kgk = 100 N/mA = 15 cm
vmax = m/s
6.Hard
3.9 kgk = 360 N/mA = 8 cm

A 3.9 kg mass on a spring with k = 360 N/m is pulled 8 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.9 kgk = 360 N/mA = 8 cm
amax = m/s²

Answer key

  1. 1. T = 0.6455 s
  2. 2. k = 12.26 N/m
  3. 3. L = 1.203 m
  4. 4. v = 1.361 m/s
  5. 5. vmax = 0.8964 m/s
  6. 6. amax = 7.385 m/s²

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