You need to do the calculation; it isn't an intuitive thing. If you write out the equation for SHM it will show you how the position varies with time. If you differentiate it wrt time, you will get the variation of velocity with time. So you can put your two values of Amplitude into that velocity equation and see what the velocities are for x= A/4. AS the differential of sin is cos, life is pretty easy for you.ual8658 said:So in class we were given a problem.
A pendulum is oscillating in SHM with amplitude A. After a while you slow it down so that its amplitude is halved. What happens to its speed at x = ± A/4 ?
The answer is 1/sqrt(5) and I don't get why.
The SHM (Simple Harmonic Motion) equation is a mathematical representation of the movement of an object that undergoes periodic motion. It is used in science to study and understand the behavior of various systems, such as a mass attached to a spring or a pendulum.
The SHM equation has three main variables: displacement (x), velocity (v), and acceleration (a). These variables can be expressed as a function of time (t) or the angular frequency (ω) and amplitude (A) of the motion.
The SHM equation can be derived from the principles of Newton's second law of motion and Hooke's law. This involves using the equations for force, acceleration, and displacement to create a differential equation, which can then be solved to obtain the SHM equation.
Yes, the SHM equation can be applied to various real-world situations, such as the motion of a pendulum, the vibrations of a guitar string, and the movement of a mass attached to a spring. It is a useful tool for predicting and analyzing the behavior of systems that undergo periodic motion.
The SHM equation assumes that the system is undergoing ideal harmonic motion, which is not always the case in real-world situations. It also does not take into account factors such as air resistance, friction, and external forces, which can affect the motion of a system. Additionally, it is a linear equation and may not accurately predict the behavior of non-linear systems.