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
4 kgk = 320 N/m

A 4 kg mass on a spring with stiffness 320 N/m oscillates on a frictionless surface. Find the frequency f.

m = 4 kgk = 320 N/m
f = Hz
2.Easy
2.4 kgk = 300 N/m

A 2.4 kg mass on a spring with stiffness 300 N/m oscillates on a frictionless surface. Find the frequency f.

m = 2.4 kgk = 300 N/m
f = Hz
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 mT = 1.88 s

An astronaut on another planet finds that a simple pendulum 1 m long has a period of 1.88 s for small swings. Find the gravitational acceleration g on that planet.

L = 1 mT = 1.88 s
g = m/s²
5.Hard
1.8 kgk = 290 N/mA = 15 cm

A 1.8 kg mass on a spring with k = 290 N/m is pulled 15 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1.8 kgk = 290 N/mA = 15 cm
E = J
6.Hard
0.6 kgk = 220 N/mA = 4 cm

A 0.6 kg mass on a spring with k = 220 N/m is pulled 4 cm from equilibrium and released. Find its maximum speed vmax.

m = 0.6 kgk = 220 N/mA = 4 cm
vmax = m/s

Answer key

  1. 1. f = 1.424 Hz
  2. 2. f = 1.779 Hz
  3. 3. L = 0.8051 m
  4. 4. g = 11.17 m/s²
  5. 5. E = 3.262 J
  6. 6. vmax = 0.7659 m/s

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