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
2.3 kgk = 370 N/m

A 2.3 kg mass on a spring with stiffness 370 N/m oscillates on a frictionless surface. Find the period T.

m = 2.3 kgk = 370 N/m
T = s
2.Easy
1.6 kgk = 320 N/m

A 1.6 kg mass on a spring with stiffness 320 N/m oscillates on a frictionless surface. Find the period T.

m = 1.6 kgk = 320 N/m
T = s
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1.1 s? Use g = 9.81 m/s². Find L.

T = 1.1 sg = 9.81 m/s²
L = m
4.Medium
t (s)x (cm)0.85 s

A 1 kg mass on a spring with k = 360 N/m is pulled 10 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 0.85 s (with sign).

m = 1 kgk = 360 N/mA = 10 cmt = 0.85 s
v = m/s
5.Hard
0.2 kgk = 300 N/mA = 14 cm

A 0.2 kg mass on a spring with k = 300 N/m is pulled 14 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 0.2 kgk = 300 N/mA = 14 cm
E = J
6.Hard
3.8 kgk = 70 N/mA = 7 cm

A 3.8 kg mass on a spring with k = 70 N/m is pulled 7 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 3.8 kgk = 70 N/mA = 7 cm
E = J

Answer key

  1. 1. T = 0.4954 s
  2. 2. T = 0.4443 s
  3. 3. L = 0.3007 m
  4. 4. v = 0.7731 m/s
  5. 5. E = 2.94 J
  6. 6. E = 0.1715 J

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