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
2.3 kgk = ?9.5 cm

Hanging a 2.3 kg mass on a spring stretches it by 9.5 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 2.3 kgx = 9.5 cmg = 9.81 m/s²
k = N/m
2.Easy
0.2 kgk = 200 N/m

A 0.2 kg mass on a spring with stiffness 200 N/m oscillates on a frictionless surface. Find the period T.

m = 0.2 kgk = 200 N/m
T = s
3.Medium
1.9 kgk = 60 N/mA = 5 cmx = 3 cm

A 1.9 kg mass on a spring with k = 60 N/m oscillates on a frictionless surface with an amplitude of 5 cm. Find its speed v when it is 3 cm from equilibrium.

m = 1.9 kgk = 60 N/mA = 5 cmx = 3 cm
v = m/s
4.Medium
L = 1.7 m

A simple pendulum has a length of 1.7 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.7 mg = 9.81 m/s²
T = s
5.Hard
3.1 kgk = 170 N/mA = 3 cm

A 3.1 kg mass on a spring with k = 170 N/m is pulled 3 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.1 kgk = 170 N/mA = 3 cm
amax = m/s²
6.Hard
0.2 kgk = 270 N/mA = 18 cm

A 0.2 kg mass on a spring with k = 270 N/m is pulled 18 cm from equilibrium and released. Find its maximum acceleration amax.

m = 0.2 kgk = 270 N/mA = 18 cm
amax = m/s²

Answer key

  1. 1. k = 237.5 N/m
  2. 2. T = 0.1987 s
  3. 3. v = 0.2248 m/s
  4. 4. T = 2.616 s
  5. 5. amax = 1.645 m/s²
  6. 6. amax = 243 m/s²

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