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
1.4 kgk = 320 N/m

A 1.4 kg mass on a spring with stiffness 320 N/m oscillates on a frictionless surface. Find the period T.

m = 1.4 kgk = 320 N/m
T = s
2.Easy
0.2 kgk

A 0.2 kg mass on a spring makes 15 complete oscillations in 44 s. Find the frequency f of the oscillation.

m = 0.2 kgN = 15t = 44 s
f = Hz
3.Medium
t (s)x (cm)1.25 s

A 1.4 kg mass on a spring with k = 250 N/m is pulled 10 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 1.25 s (with sign).

m = 1.4 kgk = 250 N/mA = 10 cmt = 1.25 s
x = cm
4.Medium
t (s)x (cm)1 s

A 1.3 kg mass on a spring with k = 380 N/m is pulled 11 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 1 s (with sign).

m = 1.3 kgk = 380 N/mA = 11 cmt = 1 s
v = m/s
5.Hard
2.5 kgk = 1000 N/m300 m/s

A 15 g bullet moving at 300 m/s hits and stays in a 2.5 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1000 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 15 gv = 300 m/sM = 2.5 kgk = 1000 N/m
A = cm
6.Hard
mk = 420 N/mA = 12 cmx = 10 cm

A mass on a spring with k = 420 N/m oscillates on a frictionless surface with an amplitude of 12 cm. Find the energy U stored in the spring when the mass is 10 cm from equilibrium.

k = 420 N/mA = 12 cmx = 10 cm
U = J

Answer key

  1. 1. T = 0.4156 s
  2. 2. f = 0.3409 Hz
  3. 3. x = −5.438 cm
  4. 4. v = 1.85 m/s
  5. 5. A = 8.973 cm
  6. 6. U = 2.1 J

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