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
0.2 kgk18 cm

Hanging a 0.2 kg mass on a spring stretches it by 18 cm. Use g = 9.81 m/s². The mass is then pulled down a little and released. Find the period T of its oscillation.

m = 0.2 kgx = 18 cmg = 9.81 m/s²
T = s
2.Easy
3.6 kgk = 390 N/m

A 3.6 kg mass on a spring with stiffness 390 N/m oscillates on a frictionless surface. Find the period T.

m = 3.6 kgk = 390 N/m
T = s
3.Medium
t (s)x (cm)0.35 s

A 1.6 kg mass on a spring with k = 60 N/m is pulled 9 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 0.35 s (with sign).

m = 1.6 kgk = 60 N/mA = 9 cmt = 0.35 s
v = m/s
4.Medium
L = 1.5 m

A simple pendulum has a length of 1.5 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.5 mg = 9.81 m/s²
T = s
5.Hard
1.7 kgk = 130 N/m

A 1.7 kg mass is attached to the lower end of an unstretched vertical spring with k = 130 N/m and released from rest. Use g = 9.81 m/s². Find the greatest extension xmax of the spring in cm.

m = 1.7 kgk = 130 N/mg = 9.81 m/s²
xmax = cm
6.Hard
mk = 470 N/mA = 20 cmx = 13 cm

A mass on a spring with k = 470 N/m oscillates on a frictionless surface with an amplitude of 20 cm. Find its kinetic energy K when it is 13 cm from equilibrium.

k = 470 N/mA = 20 cmx = 13 cm
K = J

Answer key

  1. 1. T = 0.8511 s
  2. 2. T = 0.6037 s
  3. 3. v = −0.4633 m/s
  4. 4. T = 2.457 s
  5. 5. xmax = 25.66 cm
  6. 6. K = 5.429 J

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