Question

How long must a simple pendulum be if it is to make exactly six swinan object with mass 3.4 kg is executing simple harmonic motion, attached to a spring with spring constant 260 n/m . when the object is 0.025 m from its equilibrium position, it is moving with a speed of 0.50 m/s .gs per second? (that is, one complete vibration takes exactly 0.333 s.)?

Answer 1

To find the pendulum length for six complete vibrations per second, with each vibration taking 0.333 seconds, the formula T = 2π√(L/g) is used to determine the length L. The resulting pendulum length is approximately 0.0277 m.

Step-by-step explanation:

The question is asking for the length of a simple pendulum that has a period of 0.333 seconds (which is the time taken for one complete vibration or swing back and forth). To calculate the length of the pendulum, we use the formula for the period of a simple pendulum: T = 2π√(L/g), where T is the period, L is the length of the pendulum and g is the acceleration due to gravity, which is approximately 9.80 m/s². Since we are given the period and the value of g, we can rearrange the formula to solve for the length: L = (T/(2π))² × g.

Plugging in the values, we have L = (0.333/(2π))² × 9.80, which yields the length L. After calculating, we find that the pendulum must be approximately 0.0277 m long to make exactly six swings per second since one complete vibration takes 0.333 s.