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
2.9 kgk = 30 N/m

A 2.9 kg mass on a spring with stiffness 30 N/m oscillates on a frictionless surface. Find the period T.

m = 2.9 kgk = 30 N/m
T = s
2.Easy
1.7 kgk = ?

A 1.7 kg mass on a spring oscillates with a period of 0.85 s. Find the spring stiffness k.

m = 1.7 kgT = 0.85 s
k = N/m
3.Medium
L = 0.2 m

A simple pendulum has a length of 0.2 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.2 mg = 9.81 m/s²
T = s
4.Medium
t (s)x (cm)0.7 s

A 3.3 kg mass on a spring with k = 370 N/m is pulled 7 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 0.7 s (with sign).

m = 3.3 kgk = 370 N/mA = 7 cmt = 0.7 s
v = m/s
5.Hard
3.1 kgk = 260 N/mA = 6 cm

A 3.1 kg mass on a spring with k = 260 N/m is pulled 6 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 3.1 kgk = 260 N/mA = 6 cm
E = J
6.Hard
1.5 kgk = 1900 N/m100 m/s

A 20 g bullet moving at 100 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 = 1900 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 20 gv = 100 m/sM = 1.5 kgk = 1900 N/m
A = cm

Answer key

  1. 1. T = 1.954 s
  2. 2. k = 92.89 N/m
  3. 3. T = 0.8971 s
  4. 4. v = −0.67 m/s
  5. 5. E = 0.468 J
  6. 6. A = 3.722 cm

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