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

A 2.9 kg mass on a spring makes 40 complete oscillations in 40 s. Find the frequency f of the oscillation.

m = 2.9 kgN = 40t = 40 s
f = Hz
2.Easy
2.9 kgk = 340 N/m

A 2.9 kg mass on a spring with stiffness 340 N/m oscillates on a frictionless surface. Find the frequency f.

m = 2.9 kgk = 340 N/m
f = Hz
3.Medium
1.6 kgk = 500 N/mA = 9 cmx = 3 cm

A 1.6 kg mass on a spring with k = 500 N/m oscillates on a frictionless surface with an amplitude of 9 cm. Find its speed v when it is 3 cm from equilibrium.

m = 1.6 kgk = 500 N/mA = 9 cmx = 3 cm
v = m/s
4.Medium
t (s)x (cm)0.4 s

A 2.4 kg mass on a spring with k = 80 N/m is pulled 5 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 0.4 s (with sign).

m = 2.4 kgk = 80 N/mA = 5 cmt = 0.4 s
v = m/s
5.Hard
1.5 kgk = 1800 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 = 1800 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 20 gv = 100 m/sM = 1.5 kgk = 1800 N/m
A = cm
6.Hard
3.4 kgk = 360 N/mA = 15 cm

A 3.4 kg mass on a spring with k = 360 N/m is pulled 15 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.4 kgk = 360 N/mA = 15 cm
vmax = m/s

Answer key

  1. 1. f = 1 Hz
  2. 2. f = 1.723 Hz
  3. 3. v = 1.5 m/s
  4. 4. v = −0.2134 m/s
  5. 5. A = 3.824 cm
  6. 6. vmax = 1.543 m/s

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