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
1.6 kgk = 230 N/m

A 1.6 kg mass on a spring with stiffness 230 N/m oscillates on a frictionless surface. Find the frequency f.

m = 1.6 kgk = 230 N/m
f = Hz
2.Easy
4.5 kgk = 280 N/m

A 4.5 kg mass on a spring with stiffness 280 N/m oscillates on a frictionless surface. Find the frequency f.

m = 4.5 kgk = 280 N/m
f = Hz
3.Medium
L = 2 m

A simple pendulum has a length of 2 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2 mg = 9.81 m/s²
T = s
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.2 s? Use g = 9.81 m/s². Find L.

T = 1.2 sg = 9.81 m/s²
L = m
5.Hard
3 kgk = 1200 N/m100 m/s

A 20 g bullet moving at 100 m/s hits and stays in a 3 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1200 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 20 gv = 100 m/sM = 3 kgk = 1200 N/m
A = cm
6.Hard
3.4 kgk = 340 N/mA = 5 cm

A 3.4 kg mass on a spring with k = 340 N/m is pulled 5 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.4 kgk = 340 N/mA = 5 cm
amax = m/s²

Answer key

  1. 1. f = 1.908 Hz
  2. 2. f = 1.255 Hz
  3. 3. T = 2.837 s
  4. 4. L = 0.3578 m
  5. 5. A = 3.322 cm
  6. 6. amax = 5 m/s²

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