Question

how can we prove that acceleration is directly proportional to the x.
proof:
$a \alpha x$
​

Answer 1

Answer:

Yes, we can easily proof that "a" is directly proportional to the "x".

SHM and Circular Motion

a directly proportional to x

F directly proportional to x

Then, it is simple harmonic motion

As, Ø = wt

radius is equal to the amplitude.

cosØ = x/A

=> x = A cos Ø

=> x = A cos wt

v = dx/dt

= A[-sin(wt).w]

= -wA sin (wt)

So,

a = dv/dt

a = -wA [cos (wt).w]

a = -w²A cos (wt)

So therefore,

=> a = -w²x

So, a is directly proportional to x

Therefore, it is a simple harmonic motion.

Hence Proved

Answer 2

Answer:

By the help of using the formula of simple harmonic motion we can prove it.