Question

A harmonic oscillation is represented by Y=0.26 cos (4000t+II/6) where y and t are in
mm and seconds respectively. Deduce (i) amplitude (ii) frequency (iii) angular
frequency (iv) period (v) initial phase. (0.26mm, 636.9 Hz, 4000 rad/s, 157 ms, -
​

Answer 1

Answer:

The amplitude of the oscillation is 0.26mm, which is the maximum displacement of the oscillation from its equilibrium position.

Question : A harmonic oscillation is represented by Y=0.26 cos (4000t+II/6) where y and t are in mm and seconds respectively

Explanation:

From the above question,

They have given :

The amplitude of the harmonic oscillation is 0.26 mm.

The frequency of the harmonic oscillation is 4000 Hz.

The phase shift of the harmonic oscillation is II/6 radians.

A harmonic oscillation is represented by Y=0.26 cos (4000t+II/6) where y and t are in mm and seconds respectively

It takes 0.00025 seconds to complete one oscillation.

(i) Amplitude: The amplitude is the maximum displacement of the oscillation from its equilibrium position. In this case, the amplitude is 0.26mm.

(ii) Frequency:

Frequency is the number of oscillations per second.

It is measured in hertz (Hz). In this case, the frequency is 636.9 Hz.

(iii) Angular Frequency:

Angular frequency is the rate of change of phase of the oscillation.

It is measured in radians per second (rad/s).

In this case, the angular frequency is 4000 rad/s.

(iv) Period:

Period is the time required for one complete oscillation.

It is measured in milliseconds (ms).

In this case, the period is 157 ms.

(v) Initial Phase:

Initial phase is the phase of the oscillation at time t = 0.

It is measured in radians (rad).

In this case, the initial phase is -π/6 rad.

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