In the figure, a 0.24-kg ball is suspended from a very light string 9.79 m long

Question

In the figure, a 0.24-kg ball is suspended from a very light string 9.79 m long and is puiled slightly to the left. As the ball swings without friction through the lowest part of its motion it encounters an ideal massless spring attached to the wall The spring pushes against the ball and eventually the ball is returned to its original starting position. Find the time for one complete cycle of this motion if the spring constant of the spring is 21 N/m. (Assume that once the pendulum ball hits the spring there is no effect due to the vertical movement of the ball.)

Explanation / Answer

Pendulum will complete only left side motion. Hence time taken will be

T= {2(l÷g)}÷2 Half of total time period

T= {2*3.14(9.79÷9.8)}÷2

T = 3.14 sec

Spring will complete its one complete oscillation

Time period for spring mass

T = 2(m÷k)

T = 2*3.14*(0.24÷21)

T = 0.67 sec.

Hence complete osc. Time period

= 3.14+.67 = 3.80sec ANSWER

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