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
5 kgk = ?

A 5 kg mass on a spring oscillates with a period of 1.45 s. Find the spring stiffness k.

m = 5 kgT = 1.45 s
k = N/m
2.Easy
0.5 kgk = ?

A 0.5 kg mass on a spring oscillates with a period of 1.45 s. Find the spring stiffness k.

m = 0.5 kgT = 1.45 s
k = N/m
3.Medium
t (s)x (cm)0.9 s

A 1.4 kg mass on a spring with k = 20 N/m is pulled 4 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.9 s (with sign).

m = 1.4 kgk = 20 N/mA = 4 cmt = 0.9 s
x = cm
4.Medium
t (s)x (cm)0.2 s

A 2.8 kg mass on a spring with k = 110 N/m is pulled 6 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.2 s (with sign).

m = 2.8 kgk = 110 N/mA = 6 cmt = 0.2 s
x = cm
5.Hard
2 kgk = 1400 N/m300 m/s

A 20 g bullet moving at 300 m/s hits and stays in a 2 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1400 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 20 gv = 300 m/sM = 2 kgk = 1400 N/m
A = cm
6.Hard
1.7 kgk = 210 N/mA = 14 cm

A 1.7 kg mass on a spring with k = 210 N/m is pulled 14 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1.7 kgk = 210 N/mA = 14 cm
E = J

Answer key

  1. 1. k = 93.88 N/m
  2. 2. k = 9.388 N/m
  3. 3. x = −3.865 cm
  4. 4. x = 1.872 cm
  5. 5. A = 11.28 cm
  6. 6. E = 2.058 J

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