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
1.1 kgk

A 1.1 kg mass on a spring makes 50 complete oscillations in 31 s. Find the frequency f of the oscillation.

m = 1.1 kgN = 50t = 31 s
f = Hz
2.Easy
3.5 kgk = 160 N/m

A 3.5 kg mass on a spring with stiffness 160 N/m oscillates on a frictionless surface. Find the period T.

m = 3.5 kgk = 160 N/m
T = s
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1.8 s? Use g = 9.81 m/s². Find L.

T = 1.8 sg = 9.81 m/s²
L = m
4.Medium
L = 1.8 m

A simple pendulum has a length of 1.8 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.8 mg = 9.81 m/s²
T = s
5.Hard
3.6 kgk = 140 N/mA = 18 cm

A 3.6 kg mass on a spring with k = 140 N/m is pulled 18 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 3.6 kgk = 140 N/mA = 18 cm
E = J
6.Hard
t (s)x (cm)t = ?14.4

A body oscillates in simple harmonic motion with period 0.5 s and amplitude 16 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 14.4 cm?

T = 0.5 sA = 16 cmx = 14.4 cm
t = s

Answer key

  1. 1. f = 1.613 Hz
  2. 2. T = 0.9293 s
  3. 3. L = 0.8051 m
  4. 4. T = 2.691 s
  5. 5. E = 2.268 J
  6. 6. t = 0.08911 s

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