Question

In the figure, a block weighing 16.4 N, which can slide without friction on an incline at angle ? = 30.0°, is connected to the top of the incline by a massless spring of unstretched length 0.430 m and spring constant 100 N/m. The block is initially at its equilibrium position. (a) How far from the top of the incline is the block’s equilibrium point? (b) If the block is pulled slightly down the incline and released, what is the period of the resulting oscillations?

Answer 1

                                

(a)

   according to newtons second law ofmotion

   F = k x

   kx = m g sin?

   x = m g sin? / k

      = [(16.4 N)sin30^o] / 100 N/m

      = 0.082 m

   so the distance from the top of the incline willbe

   d = 0.430 m + x

      = 0.512 m

(b)

   the period of resulting oscillation will be

   T = 2 ? ?[(16.4.0 N / 9.80 m /s²) / 100 N/m]

       = 0.8128 s