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
0.6 kgk = ?

A 0.6 kg mass on a spring oscillates with a period of 1.95 s. Find the spring stiffness k.

m = 0.6 kgT = 1.95 s
k = N/m
2.Easy
0.6 kgk = 20 N/m

A 0.6 kg mass on a spring with stiffness 20 N/m oscillates on a frictionless surface. Find the period T.

m = 0.6 kgk = 20 N/m
T = s
3.Medium
t (s)x (cm)1.3 s

A 3.5 kg mass on a spring with k = 80 N/m is pulled 11 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 1.3 s (with sign).

m = 3.5 kgk = 80 N/mA = 11 cmt = 1.3 s
x = cm
4.Medium
t (s)x (cm)0.4 s

A 3.8 kg mass on a spring with k = 20 N/m is pulled 6 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.4 s (with sign).

m = 3.8 kgk = 20 N/mA = 6 cmt = 0.4 s
x = cm
5.Hard
t (s)x (cm)t = ?7.2

A body oscillates in simple harmonic motion with period 1.2 s and amplitude 9 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 7.2 cm?

T = 1.2 sA = 9 cmx = 7.2 cm
t = s
6.Hard
0.6 kgk = 360 N/mA = 12 cm

A 0.6 kg mass on a spring with k = 360 N/m is pulled 12 cm from equilibrium and released. Find its maximum speed vmax.

m = 0.6 kgk = 360 N/mA = 12 cm
vmax = m/s

Answer key

  1. 1. k = 6.229 N/m
  2. 2. T = 1.088 s
  3. 3. x = 10.97 cm
  4. 4. x = 3.646 cm
  5. 5. t = 0.1771 s
  6. 6. vmax = 2.939 m/s

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