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
4.6 kgk = 260 N/m

A 4.6 kg mass on a spring with stiffness 260 N/m oscillates on a frictionless surface. Find the frequency f.

m = 4.6 kgk = 260 N/m
f = Hz
2.Easy
4.5 kgk = ?

A 4.5 kg mass on a spring oscillates with a period of 0.4 s. Find the spring stiffness k.

m = 4.5 kgT = 0.4 s
k = N/m
3.Medium
L = 1.9 m

A simple pendulum has a length of 1.9 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.9 mg = 9.81 m/s²
T = s
4.Medium
3.7 kgk = 490 N/mA = 19 cmx = 11 cm

A 3.7 kg mass on a spring with k = 490 N/m oscillates on a frictionless surface with an amplitude of 19 cm. Find its speed v when it is 11 cm from equilibrium.

m = 3.7 kgk = 490 N/mA = 19 cmx = 11 cm
v = m/s
5.Hard
t (s)x (cm)t = ?4.9

A body oscillates in simple harmonic motion with period 2.3 s and amplitude 7 cm. What is the shortest time t it needs to move from its maximum displacement of 7 cm to a displacement of 4.9 cm?

T = 2.3 sA = 7 cmx = 4.9 cm
t = s
6.Hard
1 kgk = 1700 N/m400 m/s

A 20 g bullet moving at 400 m/s hits and stays in a 1 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1700 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 20 gv = 400 m/sM = 1 kgk = 1700 N/m
A = cm

Answer key

  1. 1. f = 1.197 Hz
  2. 2. k = 1110 N/m
  3. 3. T = 2.765 s
  4. 4. v = 1.783 m/s
  5. 5. t = 0.2912 s
  6. 6. A = 19.21 cm

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