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The mass m in Figure P4.12 is attached to a rigid lever having negligible mass a

ID: 2993371 • Letter: T

Question

The mass m in Figure P4.12 is attached to a rigid lever having negligible mass

and negligible friction in the pivot. The input is the displacement x. When x

and ? are zero, the springs are at their free length. Assuming that ? is small,

derive the equation of motion for ? with x as the input.

The mass m in Figure P4.12 is attached to a rigid lever having negligible mass and negligible friction in the pivot. The input is the displacement x. When x and ? are zero, the springs are at their free length. Assuming that ? is small, derive the equation of motion for ? with x as the input.

Explanation / Answer

Force causing motion= force perpendicular to rod = m*g* sin theta + k2*x*cos theta + k1*x*L1/L2*cos theta

as theta is small. F= m*g*sin theta + x( K1+K2*L1/L2)

=m*g*x/L2 + x( K1+K2*L1/L2) =x {m*g/L2 + K1+K2*L1/L2 }

F=k'x => k'={m*g/L2 + K1+K2*L1/L2 }

Equation of motion

d^2x/dt^2 = - (k'/m ) *x