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
0.9 kgk = ?

A 0.9 kg mass on a spring oscillates with a period of 1.3 s. Find the spring stiffness k.

m = 0.9 kgT = 1.3 s
k = N/m
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 period T.

m = 2.9 kgk = 340 N/m
T = s
3.Medium
t (s)x (cm)1.05 s

A 3.5 kg mass on a spring with k = 30 N/m is pulled 3 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 1.05 s (with sign).

m = 3.5 kgk = 30 N/mA = 3 cmt = 1.05 s
v = m/s
4.Medium
L = ?

How long must a simple pendulum be to have a period of 0.8 s? Use g = 9.81 m/s². Find L.

T = 0.8 sg = 9.81 m/s²
L = m
5.Hard
1.3 kgk = 230 N/m

A 1.3 kg mass is attached to the lower end of an unstretched vertical spring with k = 230 N/m and released from rest. Use g = 9.81 m/s². Find the greatest extension xmax of the spring in cm.

m = 1.3 kgk = 230 N/mg = 9.81 m/s²
xmax = cm
6.Hard
mk = 160 N/mA = 18 cmx = 1 cm

A mass on a spring with k = 160 N/m oscillates on a frictionless surface with an amplitude of 18 cm. Find its kinetic energy K when it is 1 cm from equilibrium.

k = 160 N/mA = 18 cmx = 1 cm
K = J

Answer key

  1. 1. k = 21.02 N/m
  2. 2. T = 0.5803 s
  3. 3. v = −0.005925 m/s
  4. 4. L = 0.159 m
  5. 5. xmax = 11.09 cm
  6. 6. K = 2.584 J

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