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
2.7 kgk

A 2.7 kg mass on a spring makes 30 complete oscillations in 45 s. Find the frequency f of the oscillation.

m = 2.7 kgN = 30t = 45 s
f = Hz
2.Easy
1.3 kgk = 260 N/m

A 1.3 kg mass on a spring with stiffness 260 N/m oscillates on a frictionless surface. Find the period T.

m = 1.3 kgk = 260 N/m
T = s
3.Medium
t (s)x (cm)1.2 s

A 1.7 kg mass on a spring with k = 170 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 = 1.2 s (with sign).

m = 1.7 kgk = 170 N/mA = 4 cmt = 1.2 s
x = cm
4.Medium
3.1 kgk = 220 N/mA = 12 cmx = 10 cm

A 3.1 kg mass on a spring with k = 220 N/m oscillates on a frictionless surface with an amplitude of 12 cm. Find its speed v when it is 10 cm from equilibrium.

m = 3.1 kgk = 220 N/mA = 12 cmx = 10 cm
v = m/s
5.Hard
3.6 kgk = 110 N/mA = 12 cm

A 3.6 kg mass on a spring with k = 110 N/m is pulled 12 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.6 kgk = 110 N/mA = 12 cm
amax = m/s²
6.Hard
4 kgk = 1500 N/m200 m/s

A 12 g bullet moving at 200 m/s hits and stays in a 4 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1500 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 12 gv = 200 m/sM = 4 kgk = 1500 N/m
A = cm

Answer key

  1. 1. f = 0.6667 Hz
  2. 2. T = 0.4443 s
  3. 3. x = 3.375 cm
  4. 4. v = 0.5588 m/s
  5. 5. amax = 3.667 m/s²
  6. 6. A = 3.094 cm

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