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
3.5 kgk = ?

A 3.5 kg mass on a spring oscillates with a period of 1.1 s. Find the spring stiffness k.

m = 3.5 kgT = 1.1 s
k = N/m
2.Easy
0.8 kgk = 170 N/m

A 0.8 kg mass on a spring with stiffness 170 N/m oscillates on a frictionless surface. Find the period T.

m = 0.8 kgk = 170 N/m
T = s
3.Medium
t (s)x (cm)0.65 s

A 3.7 kg mass on a spring with k = 220 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 = 0.65 s (with sign).

m = 3.7 kgk = 220 N/mA = 9 cmt = 0.65 s
x = cm
4.Medium
1 kgk = 330 N/mA = 10 cmx = 8 cm

A 1 kg mass on a spring with k = 330 N/m oscillates on a frictionless surface with an amplitude of 10 cm. Find its speed v when it is 8 cm from equilibrium.

m = 1 kgk = 330 N/mA = 10 cmx = 8 cm
v = m/s
5.Hard
mk = 40 N/mA = 6 cmx = 1 cm

A mass on a spring with k = 40 N/m oscillates on a frictionless surface with an amplitude of 6 cm. Find its kinetic energy K when it is 1 cm from equilibrium.

k = 40 N/mA = 6 cmx = 1 cm
K = J
6.Hard
0.9 kgk = 460 N/mA = 13 cm

A 0.9 kg mass on a spring with k = 460 N/m is pulled 13 cm from equilibrium and released. Find its maximum acceleration amax.

m = 0.9 kgk = 460 N/mA = 13 cm
amax = m/s²

Answer key

  1. 1. k = 114.2 N/m
  2. 2. T = 0.431 s
  3. 3. x = 2.658 cm
  4. 4. v = 1.09 m/s
  5. 5. K = 0.07 J
  6. 6. amax = 66.44 m/s²

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