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
3.2 kgk = 180 N/m

A 3.2 kg mass on a spring with stiffness 180 N/m oscillates on a frictionless surface. Find the period T.

m = 3.2 kgk = 180 N/m
T = s
2.Easy
3.5 kgk

A 3.5 kg mass on a spring makes 20 complete oscillations in 34 s. Find the frequency f of the oscillation.

m = 3.5 kgN = 20t = 34 s
f = Hz
3.Medium
L = 2.4 m

A simple pendulum has a length of 2.4 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.4 mg = 9.81 m/s²
T = s
4.Medium
t (s)x (cm)0.15 s

A 2.3 kg mass on a spring with k = 180 N/m is pulled 5 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.15 s (with sign).

m = 2.3 kgk = 180 N/mA = 5 cmt = 0.15 s
x = cm
5.Hard
t (s)x (cm)t = ?3

A body oscillates in simple harmonic motion with period 3.2 s and amplitude 6 cm. What is the shortest time t it needs to move from its maximum displacement of 6 cm to a displacement of 3 cm?

T = 3.2 sA = 6 cmx = 3 cm
t = s
6.Hard
2.5 kgk = 70 N/mA = 19 cm

A 2.5 kg mass on a spring with k = 70 N/m is pulled 19 cm from equilibrium and released. Find its maximum acceleration amax.

m = 2.5 kgk = 70 N/mA = 19 cm
amax = m/s²

Answer key

  1. 1. T = 0.8378 s
  2. 2. f = 0.5882 Hz
  3. 3. T = 3.108 s
  4. 4. x = 1.207 cm
  5. 5. t = 0.5333 s
  6. 6. amax = 5.32 m/s²

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