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
0.6 kgk = 20 N/m

A 0.6 kg mass on a spring with stiffness 20 N/m oscillates on a frictionless surface. Find the period T.

m = 0.6 kgk = 20 N/m
T = s
2.Easy
4 kgk

A 4 kg mass on a spring makes 30 complete oscillations in 18 s. Find the frequency f of the oscillation.

m = 4 kgN = 30t = 18 s
f = Hz
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2.4 s? Use g = 9.81 m/s². Find L.

T = 2.4 sg = 9.81 m/s²
L = m
4.Medium
L = 1.1 m

A simple pendulum has a length of 1.1 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.1 mg = 9.81 m/s²
T = s
5.Hard
mk = 370 N/mA = 8 cmx = 6 cm

A mass on a spring with k = 370 N/m oscillates on a frictionless surface with an amplitude of 8 cm. Find its kinetic energy K when it is 6 cm from equilibrium.

k = 370 N/mA = 8 cmx = 6 cm
K = J
6.Hard
t (s)x (cm)t = ?4.9

A body oscillates in simple harmonic motion with period 3.5 s and amplitude 7 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 4.9 cm?

T = 3.5 sA = 7 cmx = 4.9 cm
t = s

Answer key

  1. 1. T = 1.088 s
  2. 2. f = 1.667 Hz
  3. 3. L = 1.431 m
  4. 4. T = 2.104 s
  5. 5. K = 0.518 J
  6. 6. t = 0.4319 s

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