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
0.4 kgk = ?

A 0.4 kg mass on a spring makes 50 complete oscillations in 34 s. Find the spring stiffness k.

m = 0.4 kgN = 50t = 34 s
k = N/m
2.Easy
3.4 kgk = 340 N/m

A 3.4 kg mass on a spring with stiffness 340 N/m oscillates on a frictionless surface. Find the period T.

m = 3.4 kgk = 340 N/m
T = s
3.Medium
3.7 kgk = 250 N/mA = 6 cmx = 4 cm

A 3.7 kg mass on a spring with k = 250 N/m oscillates on a frictionless surface with an amplitude of 6 cm. Find its speed v when it is 4 cm from equilibrium.

m = 3.7 kgk = 250 N/mA = 6 cmx = 4 cm
v = m/s
4.Medium
1.8 kgk = 100 N/mA = 18 cmx = 17 cm

A 1.8 kg mass on a spring with k = 100 N/m oscillates on a frictionless surface with an amplitude of 18 cm. Find its speed v when it is 17 cm from equilibrium.

m = 1.8 kgk = 100 N/mA = 18 cmx = 17 cm
v = m/s
5.Hard
4 kgk = 270 N/mA = 5 cm

A 4 kg mass on a spring with k = 270 N/m is pulled 5 cm from equilibrium and released. Find its maximum speed vmax.

m = 4 kgk = 270 N/mA = 5 cm
vmax = m/s
6.Hard
0.7 kgk = 130 N/mA = 17 cm

A 0.7 kg mass on a spring with k = 130 N/m is pulled 17 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 0.7 kgk = 130 N/mA = 17 cm
E = J

Answer key

  1. 1. k = 34.15 N/m
  2. 2. T = 0.6283 s
  3. 3. v = 0.3676 m/s
  4. 4. v = 0.441 m/s
  5. 5. vmax = 0.4108 m/s
  6. 6. E = 1.879 J

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