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
0.2 kgk

A 0.2 kg mass on a spring makes 30 complete oscillations in 58 s. Find the frequency f of the oscillation.

m = 0.2 kgN = 30t = 58 s
f = Hz
2.Easy
3.7 kgk = 180 N/m

A 3.7 kg mass on a spring with stiffness 180 N/m oscillates on a frictionless surface. Find the frequency f.

m = 3.7 kgk = 180 N/m
f = Hz
3.Medium
L = 0.7 mT = 1.06 s

An astronaut on another planet finds that a simple pendulum 0.7 m long has a period of 1.06 s for small swings. Find the gravitational acceleration g on that planet.

L = 0.7 mT = 1.06 s
g = m/s²
4.Medium
4 kgk = 160 N/mA = 5 cmx = 2 cm

A 4 kg mass on a spring with k = 160 N/m oscillates on a frictionless surface with an amplitude of 5 cm. Find its speed v when it is 2 cm from equilibrium.

m = 4 kgk = 160 N/mA = 5 cmx = 2 cm
v = m/s
5.Hard
3 kgk = 120 N/mA = 11 cm

A 3 kg mass on a spring with k = 120 N/m is pulled 11 cm from equilibrium and released. Find its maximum speed vmax.

m = 3 kgk = 120 N/mA = 11 cm
vmax = m/s
6.Hard
t (s)x (cm)t = ?7.5

A body oscillates in simple harmonic motion with period 3.8 s and amplitude 10 cm. What is the shortest time t it needs to move from its maximum displacement of 10 cm to a displacement of 7.5 cm?

T = 3.8 sA = 10 cmx = 7.5 cm
t = s

Answer key

  1. 1. f = 0.5172 Hz
  2. 2. f = 1.11 Hz
  3. 3. g = 24.59 m/s²
  4. 4. v = 0.2898 m/s
  5. 5. vmax = 0.6957 m/s
  6. 6. t = 0.4371 s

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