Q

# Solve this problem Which one of the following equations of motion represents simple harmonic motion?

Which one of the following equations of motion represents simple harmonic motion?

• Option 1)

Acceleration = -k(x +a)

• Option 2)

Acceleration = k(x + a)

• Option 3)

Acceleration = kx

• Option 4)

Acceleration = -k0x + k1x2

where k, k0, k1 and a are all positive.

116 Views

As discuss

Equation of S.H.M. -

$a=-\frac{d^{2}x}{dt^{2}}= -w^{2}x$

$w= \sqrt{\frac{k}{m}}$

- wherein

$x= A\sin \left ( wt+\delta \right )$

$a=-Kx$

where $x=x+a\\ a=-K(x+a)$

In S.H.M acceleration is directly proportional to the displacement from the mean position

Also the acceleration is in the opposite direction of displacement

Option 1)

Acceleration = -k(x +a)

This solution is correct

Option 2)

Acceleration = k(x + a)

This solution is incorrect

Option 3)

Acceleration = kx

This solution is incorrect

Option 4)

Acceleration = -k0x + k1x2

where k, k0, k1 and a are all positive.

This solution is incorrect

Exams
Articles
Questions