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
2.5 kgk = 170 N/m

A 2.5 kg mass on a spring with stiffness 170 N/m oscillates on a frictionless surface. Find the period T.

m = 2.5 kgk = 170 N/m
T = s
2.Easy
2 kgk = 30 N/m

A 2 kg mass on a spring with stiffness 30 N/m oscillates on a frictionless surface. Find the period T.

m = 2 kgk = 30 N/m
T = s
3.Medium
t (s)x (cm)1.45 s

A 2.5 kg mass on a spring with k = 320 N/m is pulled 13 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 1.45 s (with sign).

m = 2.5 kgk = 320 N/mA = 13 cmt = 1.45 s
x = cm
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2.9 s? Use g = 9.81 m/s². Find L.

T = 2.9 sg = 9.81 m/s²
L = m
5.Hard
2.1 kgk = 260 N/mA = 4 cm

A 2.1 kg mass on a spring with k = 260 N/m is pulled 4 cm from equilibrium and released. Find its maximum speed vmax.

m = 2.1 kgk = 260 N/mA = 4 cm
vmax = m/s
6.Hard
0.7 kgk = 20 N/mA = 8 cm

A 0.7 kg mass on a spring with k = 20 N/m is pulled 8 cm from equilibrium and released. Find its maximum acceleration amax.

m = 0.7 kgk = 20 N/mA = 8 cm
amax = m/s²

Answer key

  1. 1. T = 0.7619 s
  2. 2. T = 1.622 s
  3. 3. x = −9.969 cm
  4. 4. L = 2.09 m
  5. 5. vmax = 0.4451 m/s
  6. 6. amax = 2.286 m/s²

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