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
1.9 kgk = ?

A 1.9 kg mass on a spring oscillates with a period of 0.35 s. Find the spring stiffness k.

m = 1.9 kgT = 0.35 s
k = N/m
2.Easy
4.7 kgk = 90 N/m

A 4.7 kg mass on a spring with stiffness 90 N/m oscillates on a frictionless surface. Find the frequency f.

m = 4.7 kgk = 90 N/m
f = Hz
3.Medium
L = 0.8 m

A simple pendulum has a length of 0.8 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.8 mg = 9.81 m/s²
T = s
4.Medium
L = ?

How long must a simple pendulum be to have a period of 3 s? Use g = 9.81 m/s². Find L.

T = 3 sg = 9.81 m/s²
L = m
5.Hard
2.5 kgk = 340 N/mA = 18 cm

A 2.5 kg mass on a spring with k = 340 N/m is pulled 18 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 2.5 kgk = 340 N/mA = 18 cm
E = J
6.Hard
3.5 kgk = 1100 N/m150 m/s

A 10 g bullet moving at 150 m/s hits and stays in a 3.5 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1100 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 10 gv = 150 m/sM = 3.5 kgk = 1100 N/m
A = cm

Answer key

  1. 1. k = 612.3 N/m
  2. 2. f = 0.6965 Hz
  3. 3. T = 1.794 s
  4. 4. L = 2.236 m
  5. 5. E = 5.508 J
  6. 6. A = 2.414 cm

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