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
1.9 kgk = ?

A 1.9 kg mass on a spring oscillates with a period of 2.2 s. Find the spring stiffness k.

m = 1.9 kgT = 2.2 s
k = N/m
2.Easy
1.7 kgk = 250 N/m

A 1.7 kg mass on a spring with stiffness 250 N/m oscillates on a frictionless surface. Find the frequency f.

m = 1.7 kgk = 250 N/m
f = Hz
3.Medium
0.7 kgk = 140 N/mA = 6 cmx = 4 cm

A 0.7 kg mass on a spring with k = 140 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 = 0.7 kgk = 140 N/mA = 6 cmx = 4 cm
v = m/s
4.Medium
t (s)x (cm)1.5 s

A 1.7 kg mass on a spring with k = 220 N/m is pulled 5 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 1.5 s (with sign).

m = 1.7 kgk = 220 N/mA = 5 cmt = 1.5 s
v = m/s
5.Hard
3.7 kgk = 290 N/mA = 12 cm

A 3.7 kg mass on a spring with k = 290 N/m is pulled 12 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.7 kgk = 290 N/mA = 12 cm
vmax = m/s
6.Hard
2.2 kgk = 200 N/mA = 17 cm

A 2.2 kg mass on a spring with k = 200 N/m is pulled 17 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 2.2 kgk = 200 N/mA = 17 cm
E = J

Answer key

  1. 1. k = 15.5 N/m
  2. 2. f = 1.93 Hz
  3. 3. v = 0.6325 m/s
  4. 4. v = 0.5557 m/s
  5. 5. vmax = 1.062 m/s
  6. 6. E = 2.89 J

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