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
1.4 kgk17.5 cm

Hanging a 1.4 kg mass on a spring stretches it by 17.5 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 = 1.4 kgx = 17.5 cmg = 9.81 m/s²
T = s
2.Easy
1.7 kgk = 350 N/m

A 1.7 kg mass on a spring with stiffness 350 N/m oscillates on a frictionless surface. Find the period T.

m = 1.7 kgk = 350 N/m
T = s
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1.9 s? Use g = 9.81 m/s². Find L.

T = 1.9 sg = 9.81 m/s²
L = m
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.2 s? Use g = 9.81 m/s². Find L.

T = 1.2 sg = 9.81 m/s²
L = m
5.Hard
1.1 kgk = 370 N/mA = 18 cm

A 1.1 kg mass on a spring with k = 370 N/m is pulled 18 cm from equilibrium and released. Find its maximum speed vmax.

m = 1.1 kgk = 370 N/mA = 18 cm
vmax = m/s
6.Hard
0.6 kgk = 160 N/mA = 4 cm

A 0.6 kg mass on a spring with k = 160 N/m is pulled 4 cm from equilibrium and released. Find its maximum acceleration amax.

m = 0.6 kgk = 160 N/mA = 4 cm
amax = m/s²

Answer key

  1. 1. T = 0.8392 s
  2. 2. T = 0.4379 s
  3. 3. L = 0.897 m
  4. 4. L = 0.3578 m
  5. 5. vmax = 3.301 m/s
  6. 6. amax = 10.67 m/s²

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