Which of the following functions represent `SHM` :- (i) `sin 2omegat` , (ii) `sin omegat + 2cos omegat` , (iii) `sinomegat + cos 2omegat`
Text Solution
AI Generated Solution
To determine which of the given functions represents Simple Harmonic Motion (SHM), we need to check if the second derivative of each function is proportional to its negative value. This means we need to verify if:
\[ \frac{d^2y}{dt^2} = -k \cdot y \]
where \( k \) is a constant.
Let's analyze each function step by step.
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Which of the following equations can form stationary waves? (i) y= A sin (omegat - kx) (ii) y= A cos (omegat - kx) (iii) y= A sin (omegat + kx) (iv) y= A cos (omegat - kx) .
Find the average value in the following cases (i) i=4+3 cos omegat (ii) 5sinomegat + 2sin2omegat + 3sin3omegat (iv) V= cosomegat + 3cos2omegat + 3cos3omegat + 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))
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
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 any positive constant). ltbr. (a) sinomegat-cosomegat) (b) sin^(3)omegat (c) 3cos((pi)/(4)-2omegat) (d) cosomegat+cos3omegat+cos5omegat) (e) exp(-omega^(2)t^(2)) (f) 1+omegat+omega^(2)t^(2)
Out of the following functions representing motion of a particle which represents SHM? 1. x=sin^(3)omegat 2. x=1+omegat+omega^(2)t^(2) 3. x=cosomegat+cos3omegat+cos5omegat 4. x=sinomegat+cosomegat
