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
4.5 kgk = 370 N/m

A 4.5 kg mass on a spring with stiffness 370 N/m oscillates on a frictionless surface. Find the frequency f.

m = 4.5 kgk = 370 N/m
f = Hz
2.Easy
0.3 kgk = ?

A 0.3 kg mass on a spring makes 10 complete oscillations in 6 s. Find the spring stiffness k.

m = 0.3 kgN = 10t = 6 s
k = N/m
3.Medium
t (s)x (cm)1.45 s

A 1.7 kg mass on a spring with k = 300 N/m is pulled 9 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 1.45 s (with sign).

m = 1.7 kgk = 300 N/mA = 9 cmt = 1.45 s
x = cm
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2.6 s? Use g = 9.81 m/s². Find L.

T = 2.6 sg = 9.81 m/s²
L = m
5.Hard
0.8 kgk = 210 N/mA = 4 cm

A 0.8 kg mass on a spring with k = 210 N/m is pulled 4 cm from equilibrium and released. Find its maximum acceleration amax.

m = 0.8 kgk = 210 N/mA = 4 cm
amax = m/s²
6.Hard
1 kgk = 1300 N/m500 m/s

An 8 g bullet moving at 500 m/s hits and stays in a 1 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1300 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 8 gv = 500 m/sM = 1 kgk = 1300 N/m
A = cm

Answer key

  1. 1. f = 1.443 Hz
  2. 2. k = 32.9 N/m
  3. 3. x = 8.245 cm
  4. 4. L = 1.68 m
  5. 5. amax = 10.5 m/s²
  6. 6. A = 11.05 cm

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