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A 4-lb collar can slide without friction along a horizontal rod and is in equilibrium at A when it is pushed 1 in. to the right and released from rest. The springs are undeformed when the collar is at A and the constant of each spring is 2800 lb/in. Determine the maximum velocity of the collar.

Answer :

Onyebuchinnajigo

The maximum velocity of the collar is 0.335 m/s.

Maximum velocity of simple harmonic motion

The maximum velocity of a simple harmonic motion occurs when the object is in equilibrium position.

K.E = U

¹/₂mv² = ¹/₂kx²

mv² = kx²

where;

  • k is spring constant = 2800 lb/in = 316.36 N/m
  • x is extension = 1 in = 0.0254 m
  • m is mass = 4 lb = 1.81 kg

[tex]v = \sqrt{\frac{kx^2}{m} } \\\\v = \sqrt{\frac{316.36 \times 0.0254^2}{1.81} }\\\\v = 0.335 \ m/s[/tex]

Thus, the maximum velocity of the collar is 0.335 m/s.

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