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
1.7 kgk = ?

A 1.7 kg mass on a spring makes 25 complete oscillations in 52 s. Find the spring stiffness k.

m = 1.7 kgN = 25t = 52 s
k = N/m
2.Easy
4.5 kgk = ?

A 4.5 kg mass on a spring oscillates with a period of 1 s. Find the spring stiffness k.

m = 4.5 kgT = 1 s
k = N/m
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1.1 s? Use g = 9.81 m/s². Find L.

T = 1.1 sg = 9.81 m/s²
L = m
4.Medium
0.6 kgk = 450 N/mA = 13 cmx = 8 cm

A 0.6 kg mass on a spring with k = 450 N/m oscillates on a frictionless surface with an amplitude of 13 cm. Find its speed v when it is 8 cm from equilibrium.

m = 0.6 kgk = 450 N/mA = 13 cmx = 8 cm
v = m/s
5.Hard
t (s)x (cm)t = ?6

A body oscillates in simple harmonic motion with period 2.8 s and amplitude 20 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 6 cm?

T = 2.8 sA = 20 cmx = 6 cm
t = s
6.Hard
mk = 180 N/mA = 9 cmx = 3 cm

A mass on a spring with k = 180 N/m oscillates on a frictionless surface with an amplitude of 9 cm. Find the energy U stored in the spring when the mass is 3 cm from equilibrium.

k = 180 N/mA = 9 cmx = 3 cm
U = J

Answer key

  1. 1. k = 15.51 N/m
  2. 2. k = 177.7 N/m
  3. 3. L = 0.3007 m
  4. 4. v = 2.806 m/s
  5. 5. t = 0.1358 s
  6. 6. U = 0.081 J

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