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
0.8 kgk = ?16.5 cm

Hanging a 0.8 kg mass on a spring stretches it by 16.5 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 0.8 kgx = 16.5 cmg = 9.81 m/s²
k = N/m
2.Easy
5 kgk = 180 N/m

A 5 kg mass on a spring with stiffness 180 N/m oscillates on a frictionless surface. Find the period T.

m = 5 kgk = 180 N/m
T = s
3.Medium
t (s)x (cm)1.1 s

A 2.6 kg mass on a spring with k = 370 N/m is pulled 9 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 1.1 s (with sign).

m = 2.6 kgk = 370 N/mA = 9 cmt = 1.1 s
x = cm
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2 s? Use g = 9.81 m/s². Find L.

T = 2 sg = 9.81 m/s²
L = m
5.Hard
0.9 kgk = 460 N/mA = 19 cm

A 0.9 kg mass on a spring with k = 460 N/m is pulled 19 cm from equilibrium and released. Find its maximum acceleration amax.

m = 0.9 kgk = 460 N/mA = 19 cm
amax = m/s²
6.Hard
2.3 kgk = 370 N/mA = 18 cm

A 2.3 kg mass on a spring with k = 370 N/m is pulled 18 cm from equilibrium and released. Find its maximum acceleration amax.

m = 2.3 kgk = 370 N/mA = 18 cm
amax = m/s²

Answer key

  1. 1. k = 47.56 N/m
  2. 2. T = 1.047 s
  3. 3. x = 7.645 cm
  4. 4. L = 0.994 m
  5. 5. amax = 97.11 m/s²
  6. 6. amax = 28.96 m/s²

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