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
2.1 kgk = 320 N/m

A 2.1 kg mass on a spring with stiffness 320 N/m oscillates on a frictionless surface. Find the period T.

m = 2.1 kgk = 320 N/m
T = s
2.Easy
2.4 kgk = 330 N/m

A 2.4 kg mass on a spring with stiffness 330 N/m oscillates on a frictionless surface. Find the frequency f.

m = 2.4 kgk = 330 N/m
f = Hz
3.Medium
3.7 kgk = 340 N/mA = 7 cmx = 1 cm

A 3.7 kg mass on a spring with k = 340 N/m oscillates on a frictionless surface with an amplitude of 7 cm. Find its speed v when it is 1 cm from equilibrium.

m = 3.7 kgk = 340 N/mA = 7 cmx = 1 cm
v = m/s
4.Medium
t (s)x (cm)1.1 s

A 1.4 kg mass on a spring with k = 360 N/m is pulled 12 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 1.1 s (with sign).

m = 1.4 kgk = 360 N/mA = 12 cmt = 1.1 s
x = cm
5.Hard
2.6 kgk = 180 N/m

A 2.6 kg mass is attached to the lower end of an unstretched vertical spring with k = 180 N/m and released from rest. Use g = 9.81 m/s². Find the greatest extension xmax of the spring in cm.

m = 2.6 kgk = 180 N/mg = 9.81 m/s²
xmax = cm
6.Hard
3.9 kgk = 310 N/mA = 19 cm

A 3.9 kg mass on a spring with k = 310 N/m is pulled 19 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 3.9 kgk = 310 N/mA = 19 cm
E = J

Answer key

  1. 1. T = 0.509 s
  2. 2. f = 1.866 Hz
  3. 3. v = 0.6641 m/s
  4. 4. x = 4.233 cm
  5. 5. xmax = 28.34 cm
  6. 6. E = 5.596 J

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