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 kgk = 290 N/m

A 2 kg mass on a spring with stiffness 290 N/m oscillates on a frictionless surface. Find the period T.

m = 2 kgk = 290 N/m
T = s
2.Easy
2.1 kgk = ?

A 2.1 kg mass on a spring oscillates with a period of 1.85 s. Find the spring stiffness k.

m = 2.1 kgT = 1.85 s
k = N/m
3.Medium
0.2 kgk = 350 N/mA = 11 cmx = 6 cm

A 0.2 kg mass on a spring with k = 350 N/m oscillates on a frictionless surface with an amplitude of 11 cm. Find its speed v when it is 6 cm from equilibrium.

m = 0.2 kgk = 350 N/mA = 11 cmx = 6 cm
v = m/s
4.Medium
t (s)x (cm)0.45 s

A 3.4 kg mass on a spring with k = 180 N/m is pulled 15 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.45 s (with sign).

m = 3.4 kgk = 180 N/mA = 15 cmt = 0.45 s
x = cm
5.Hard
t (s)x (cm)t = ?3.3

A body oscillates in simple harmonic motion with period 1.6 s and amplitude 11 cm. What is the shortest time t it needs to move from its maximum displacement of 11 cm to a displacement of 3.3 cm?

T = 1.6 sA = 11 cmx = 3.3 cm
t = s
6.Hard
2 kgk = 300 N/m

A 2 kg mass is attached to the lower end of an unstretched vertical spring with k = 300 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 2 kgk = 300 N/mg = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. T = 0.5218 s
  2. 2. k = 24.22 N/m
  3. 3. v = 3.857 m/s
  4. 4. x = −14.87 cm
  5. 5. t = 0.3224 s
  6. 6. vmax = 0.801 m/s

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