The legend said:Try drawing it out yourself and post it here... as per PF rules you got to do something on your own before you get any help.
vela said:Since you're looking for a time, energy methods generally aren't very helpful. Also, for a pendulum, simple harmonic motion follows from the assumption of small amplitude vibrations — in other words, when θ is small. In this problem, that assumption doesn't hold.
Simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement from equilibrium. This means that the object will oscillate back and forth around a central point, with the same period of oscillation and amplitude each time.
Some examples of simple harmonic motion include the motion of a pendulum, a mass on a spring, and the motion of a mass attached to a vertical hanging spring. Any object that follows Hooke's Law, which states that the restoring force is directly proportional to the displacement, will exhibit simple harmonic motion.
The equation for simple harmonic motion is x = A*cos(ωt+φ), where x is the displacement from equilibrium, A is the amplitude, ω is the angular frequency, and φ is the phase constant. This equation describes the sinusoidal motion of the object.
The period of a simple harmonic motion is the time it takes for one complete oscillation, while the frequency is the number of oscillations per unit time. The relationship between the two is T = 1/f, where T is the period and f is the frequency. This means that as the frequency increases, the period decreases, and vice versa.
The amplitude of simple harmonic motion is the maximum displacement from equilibrium. A larger amplitude will result in a greater maximum velocity and acceleration, but the period and frequency will remain the same. In other words, changing the amplitude does not affect the time it takes for one complete oscillation.