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
1.3 kgk = ?3 cm

Hanging a 1.3 kg mass on a spring stretches it by 3 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 1.3 kgx = 3 cmg = 9.81 m/s²
k = N/m
2.Easy
0.6 kgk = ?

A 0.6 kg mass on a spring oscillates with a period of 0.85 s. Find the spring stiffness k.

m = 0.6 kgT = 0.85 s
k = N/m
3.Medium
3.6 kgk = 290 N/mA = 20 cmx = 6 cm

A 3.6 kg mass on a spring with k = 290 N/m oscillates on a frictionless surface with an amplitude of 20 cm. Find its speed v when it is 6 cm from equilibrium.

m = 3.6 kgk = 290 N/mA = 20 cmx = 6 cm
v = m/s
4.Medium
2.3 kgk = 140 N/mA = 19 cmx = 10 cm

A 2.3 kg mass on a spring with k = 140 N/m oscillates on a frictionless surface with an amplitude of 19 cm. Find its speed v when it is 10 cm from equilibrium.

m = 2.3 kgk = 140 N/mA = 19 cmx = 10 cm
v = m/s
5.Hard
2.1 kgk = 460 N/mA = 18 cm

A 2.1 kg mass on a spring with k = 460 N/m is pulled 18 cm from equilibrium and released. Find its maximum acceleration amax.

m = 2.1 kgk = 460 N/mA = 18 cm
amax = m/s²
6.Hard
2.1 kgk = 230 N/mA = 11 cm

A 2.1 kg mass on a spring with k = 230 N/m is pulled 11 cm from equilibrium and released. Find its maximum speed vmax.

m = 2.1 kgk = 230 N/mA = 11 cm
vmax = m/s

Answer key

  1. 1. k = 425.1 N/m
  2. 2. k = 32.78 N/m
  3. 3. v = 1.712 m/s
  4. 4. v = 1.26 m/s
  5. 5. amax = 39.43 m/s²
  6. 6. vmax = 1.151 m/s

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