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
4.9 kgk = 340 N/m

A 4.9 kg mass on a spring with stiffness 340 N/m oscillates on a frictionless surface. Find the frequency f.

m = 4.9 kgk = 340 N/m
f = Hz
2.Easy
1 kgk = ?

A 1 kg mass on a spring oscillates with a period of 1.45 s. Find the spring stiffness k.

m = 1 kgT = 1.45 s
k = N/m
3.Medium
L = 0.5 mT = 0.89 s

An astronaut on another planet finds that a simple pendulum 0.5 m long has a period of 0.89 s for small swings. Find the gravitational acceleration g on that planet.

L = 0.5 mT = 0.89 s
g = m/s²
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2 s? Use g = 9.81 m/s². Find L.

T = 2 sg = 9.81 m/s²
L = m
5.Hard
1 kgk = 310 N/mA = 10 cm

A 1 kg mass on a spring with k = 310 N/m is pulled 10 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1 kgk = 310 N/mA = 10 cm
E = J
6.Hard
3.5 kgk = 270 N/mA = 20 cm

A 3.5 kg mass on a spring with k = 270 N/m is pulled 20 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.5 kgk = 270 N/mA = 20 cm
vmax = m/s

Answer key

  1. 1. f = 1.326 Hz
  2. 2. k = 18.78 N/m
  3. 3. g = 24.92 m/s²
  4. 4. L = 0.994 m
  5. 5. E = 1.55 J
  6. 6. vmax = 1.757 m/s

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