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Give the time period for the functions g...

Give the time period for the functions given below, which are simple harmonic in nature:
`e^(-omegat)`
(ii) `log(omegat)`
(iii) `sin omegat + cos omegat`

Text Solution

AI Generated Solution

To solve the question of finding the time period for the given functions, we need to analyze each function to determine whether it exhibits simple harmonic motion (SHM) and, if so, calculate the time period. ### Step-by-Step Solution: 1. **Function (i): \( e^{-\omega t} \)** - This function represents an exponential decay. - To determine if it is periodic, we check if it repeats its values over time. - As \( t \) increases, \( e^{-\omega t} \) approaches 0 and does not repeat any values. ...
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Which of the following function of time represent (a) periodic and (b) non-periodic motion? Give the period for each case of periodic motion. [w is any positive constant]. (i) sin omegat + cos omegat (ii) sin omegat + sin2 omegat + sin4omegat (iii) e^(-omegat) (iv)log(omegat)

Which of the following functions represent SHM :- (i) sin 2omegat , (ii) sin omegat + 2cos omegat , (iii) sinomegat + cos 2omegat

Knowledge Check

  • The epoch of a simple harmonic motion represented by x = sqrt(3)sin omegat + cos omega t m is

    A
    `30^(@)`
    B
    `40.3^(@)`
    C
    `60^(@)`
    D
    `25^(@)`

  • Funcation x=A sin^(2) omegat+B cos^(2) omegat+ C sin omegat cos omegat Represents SHM.

    A
    For any value of A, B and C (except C = 0).
    B
    If A=B,C=2B and amplitude= `|Bsqrt2|`
    C
    If A=B,C=0
    D
    If A=B,C=2B amplitude=|B|.

  • Find the resultant amplitude of the following simple harmonic equations: x_(1)=5 sin omegat x_(2)=5 sin (omgat+53^(@)) x_(3)=-10 cos omegat

    A
    5
    B
    10
    C
    15
    D
    20

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    What is the time period for the function f(t) = sin omegat + cos omega t may represent the simple harmonic motion ?

    Which of the following functions of time represent (a) simple harmonic (b) periodic but not simple harmonic and (c ) non periodic motion? Give period for each case of periodic motion (omega is nay positive constant) (1) Sin^(3) omegat (2) 3cos (pi//4 -2 omegat) (3) cos omegat +cos 3 omegat + cos 5 omegat (4) e^(-omega^(2)t^(2)) (5) 1 + omegat +omega^(2) t^(2)

    Which of the following functions represent (a) periodic motion, b) simple harmonic, (c) non-periodic, (d) periodic but not simple harmonic (i) sin^(2)omegat (ii) sin 2omegat + cos 2omegat (iii) cos(4omegat + (pi)/(6))

    Which of the following functions of time represents (a) simple harmonic motion and (b) periodic motion? Given the period for each case. i. Sin omega t - cos omegat ii. Sin^(2)omegat

    What is the phase difference between two simple harmonic motions represented by x_(1) = A sin(omega t + pi/6) and x_(2) = A cos (omegat) ?

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