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
2.6 kgk = 50 N/m

A 2.6 kg mass on a spring with stiffness 50 N/m oscillates on a frictionless surface. Find the period T.

m = 2.6 kgk = 50 N/m
T = s
2.Easy
0.4 kgk = ?

A 0.4 kg mass on a spring oscillates with a period of 2.5 s. Find the spring stiffness k.

m = 0.4 kgT = 2.5 s
k = N/m
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2.3 s? Use g = 9.81 m/s². Find L.

T = 2.3 sg = 9.81 m/s²
L = m
4.Medium
L = 1.6 m

A simple pendulum has a length of 1.6 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.6 mg = 9.81 m/s²
T = s
5.Hard
2 kgk = 170 N/mA = 13 cm

A 2 kg mass on a spring with k = 170 N/m is pulled 13 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 2 kgk = 170 N/mA = 13 cm
E = J
6.Hard
1.5 kgk = 1700 N/m300 m/s

An 8 g bullet moving at 300 m/s hits and stays in a 1.5 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1700 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 8 gv = 300 m/sM = 1.5 kgk = 1700 N/m
A = cm

Answer key

  1. 1. T = 1.433 s
  2. 2. k = 2.527 N/m
  3. 3. L = 1.315 m
  4. 4. T = 2.537 s
  5. 5. E = 1.437 J
  6. 6. A = 4.74 cm

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