The figure shows a uniform beam of mass m pivoted at its lower end, with a horiz

Question

The figure shows a uniform beam of mass m pivoted at its lower end, with a horizontal spring attached between its top end and a vertical wall. The beam makes an angle with the horizontal.

(a) Find expression for the distance d the spring is stretched from equilibrium. (Use any variable or symbol stated above along with the following as necessary: k and g.)
d =

(b) Find expressions for the components of the force exerted by the pivot on the beam. (Use the following as necessary: m, k, g, and .)

=

PLEASE SHOW ALL FORMULAS AND COMPUTATIONS. THANKS

=

PLEASE SHOW ALL FORMULAS AND COMPUTATIONS. THANKS

Explanation / Answer

(a) we take sum of the moments about the hinge:
M = 0 = k*d*L*sin - m*g*½*L*cos
where L is the length of the beam, which cancels anyway.
d = mgcos / 2ksin = mg / 2ktan

(b) horizontal component Rx = kd
vertical component Ry = mg

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