Question

The spring of constant k = 170 N/m is attached to both the support and the 1.5-kg cylinder, which slides freely on the horizontal guide. If a constant 14-N force is applied to the cylinder at time t = 0 when the spring is undeformed and the system is at rest, determine the velocity of the cylinder when x = 65 mm. Also determine the maximum displacement of the cylinder.

Answer 1

Answer:

Velocity at 64 mm is 0.532 m/s

Maximum displacement = 0.082 m or 82 mm

Explanation:

The maximum displacement or amplitude is determined by the applied force from Hooke's law

$F = kA$

$A=\dfrac{F}{k}=\dfrac{14 \text{ N}}{170 \text{ N/m}}=0.082 \text{ m}$

The velocity at at any point, x, is given by

$v=\sqrt{\dfrac{k}{m}(A^2 - x^2)}$

m is the mass of the load, here the cylinder.

In fact, the expression $\sqrt{\dfrac{k}{m}}$ represents the angular velocity, $\omega$.

Substituting given values,

$v=\sqrt{\dfrac{170}{1.5}(0.082^2 - 0.065^2)} = 0.532 \text{ m/s}$