Question

x =sin³wt


represent shm??? ​

Answer 1

Answer:

(a) y = sinwt - coswt .

= √2 {

2

1

sinwt -

2

1

coswt}

= √2{cos45°.sinwt - sin45°.coswt}

= √2sin(wt - 45°)

This is in the form of y = Asin(wt ± ∅)

So, this is the equation of SHM .

Period =

ω

2π

(b) sin³wt

Use formula of sin3x = 3sinx - 4sin³x

So, sin³wt =

4

1

[ 3sinwt - sin3wt ]

Hence, you observed that this equation is a combination of two SHM. Hence, this is not SHM. But periodic motion.

Period = LCM of period { sinwt , sin3wt }

Period of sinwt =

ω

2π

period of sin3wt =

3ω

2π

so, period =

ω

2π

(c) 5cos(

4

3π

- 3wt)

= 5cos {-(3wt-

4

3π

)}

= 5cos(3wt -

4

3π

) [ cos(-∅) = cos∅]

Hence, this is SHM .

Period =

2ω

2π

=

ω

π

(d) x = 1 + wt + w²t²

At x →∞ , t→∞

There is no repetation of values . hence, this neither periodic nor SHM.