How do you know when to use sin or cos in simple harmonic motion?

How do you know when to use sin or cos in simple harmonic motion?

1) if the oscillations are noted starting from the maximum amplitude in initial position, use cosine equation. 2) if the oscillations are being noted from mean position i.e. minimum displacement in initial position, use sine equation.

What is the equation for displacement in simple harmonic motion?

Displacement as a function of time in SHM is given byx(t)=Acos(2πTt+φ)=Acos(ωt+φ) x ( t ) = A cos ( 2 π T t + φ ) = A cos ( ω t + φ ) .

What is X A cos wt?

x(t) = A cos(ωt + φ). A is the amplitude of the oscillation, i.e. the maximum displacement of the object from equilibrium, either in the positive or negative x-direction.

What is displacement equation?

Displacement is defined to be the change in position of an object. It can be defined mathematically with the following equation: Displacement = Δ x = x f − x 0 \text{Displacement}=\Delta x=x_f-x_0 Displacement=Δx=xf−x0. x f x_f xf​x, start subscript, f, end subscript refers to the value of the final position.

When the displacement of a simple harmonic oscillator is half of its amplitude?

When the displacement of a simple harmonic oscillator is half of its amplitude, its potential energy is 3J.

What is the time taken by a particle executing SHM?

A particle is executing SHM of periodic time T the time taken by a particle in moving from mean position to half the maximum displacement is (sin 30^(@)=0.5) t=T12.

Can the amplitude A and phase constant Ф be determined for an oscillator if only the position is specified at t 0 explain?

The phase constant of an oscillator determines the starting position of the oscillator, i.e. it determines the displacement at time t = 0. If we know the amplitude and phase constant of the oscillator at any given time we can determine all aspects of the oscillator completely.

What is Omega T in SHM?

It says that the displacement is equal to the amplitude of the variation, A, otherwise known as the maximum displacement, multiplied by sine omega-t, where omega is the angular frequency of the variation, and t is the time. This displacement can be in the x-direction or the y-direction, depending on the situation.

Why is Max velocity AW?

where v is the velocity of the particle, a is the amplitude and x is the distance from O. Hence the maximum velocity is aw (put x = 0 in the above equation and take the square root). The period of the motion is the time it takes for the particle to perform one complete cycle.

What is the expression for displacement velocity and acceleration in SHM?

The curve between displacement and velocity of a particle executing the simple harmonic motion is an ellipse. When ω = 1 then, the curve between v and x will be circular. Hence the expression for displacement, velocity and acceleration in linear simple harmonic motion are The system that executes SHM is called the harmonic oscillator.

How do you find the period of an oscillation in SHM?

The block begins to oscillate in SHM between where A is the amplitude of the motion and T is the period of the oscillation. The period is the time for one oscillation. (Figure) shows the motion of the block as it completes one and a half oscillations after release.

How do you find the velocity of a spring in SHM?

The velocity of the mass on a spring, oscillating in SHM, can be found by taking the derivative of the position equation: Because the sine function oscillates between –1 and +1, the maximum velocity is the amplitude times the angular frequency,

What factors affect the period and frequency of SHM?

In fact, the mass m and the force constant k are the only factors that affect the period and frequency of SHM. To derive an equation for the period and the frequency, we must first define and analyze the equations of motion.