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
4.3 kgk = 370 N/m

A 4.3 kg mass on a spring with stiffness 370 N/m oscillates on a frictionless surface. Find the period T.

m = 4.3 kgk = 370 N/m
T = s
2.Easy
4.5 kgk = 350 N/m

A 4.5 kg mass on a spring with stiffness 350 N/m oscillates on a frictionless surface. Find the period T.

m = 4.5 kgk = 350 N/m
T = s
3.Medium
2.2 kgk = 30 N/mA = 10 cmx = 5 cm

A 2.2 kg mass on a spring with k = 30 N/m oscillates on a frictionless surface with an amplitude of 10 cm. Find its speed v when it is 5 cm from equilibrium.

m = 2.2 kgk = 30 N/mA = 10 cmx = 5 cm
v = m/s
4.Medium
t (s)x (cm)1.45 s

A 1.8 kg mass on a spring with k = 380 N/m is pulled 14 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 1.45 s (with sign).

m = 1.8 kgk = 380 N/mA = 14 cmt = 1.45 s
v = m/s
5.Hard
3.2 kgk = 110 N/mA = 7 cm

A 3.2 kg mass on a spring with k = 110 N/m is pulled 7 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.2 kgk = 110 N/mA = 7 cm
amax = m/s²
6.Hard
2.5 kgk = 280 N/m

A 2.5 kg mass is attached to the lower end of an unstretched vertical spring with k = 280 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 2.5 kgk = 280 N/mg = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. T = 0.6774 s
  2. 2. T = 0.7124 s
  3. 3. v = 0.3198 m/s
  4. 4. v = −1.622 m/s
  5. 5. amax = 2.406 m/s²
  6. 6. vmax = 0.927 m/s

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