Question

Problem 6

Answer 1

Given information

Oscillations are a type of movement, very specifically periodic motion, which repeats itself after some time. Oscillations are known as vibrations also. The simplest example is the simple harmonic motion or SHM.

Step-by-step explanation

Step 1.

A basic harmonic motion of an item about an equilibrium point is represented by a second-order differential equation of the form . The displacement of the item from its equilibrium position, acceleration of the object, and angular frequency of the object performing simple harmonic motion are all represented by the letters in this equation. An item is driven in simple harmonic motion about equilibrium or mean position by a force of the kind . The restoring force constant, , has a negative sign, indicating that the force is always directed towards the equilibrium position.

, the universal solution of the second-order differential equation, gives the displacement of an object in simple harmonic motion at any given time. The amplitude of the item from its mean location is denoted by the letter .

 

The first derivative of the position function offers the object's immediate velocity, whereas the second derivative gives the object's instantaneous acceleration.