Two masses $m_{1}$ and $m_{2}$ are suspended together by a massless spring of spring constant $k$ (Fig). When the masses are in equilibrium, $m_{1}$ is removed without disturbing the system. Find the angular frequency and amplitude of oscillation of $m_{2}$ .

Open in App

Solution

As it is given that masses $m_{1}$ and $m_{2}$ are in equilibrium, initially there is no motion. Which means that there will be no angular velocity in the initial position.

When $m_{1}$ is removed equilibrium will be disturbed and an angular velocity is produced and it will revolve in a circle

We know the formula for angular frequency of an object

$ω = \sqrt{\frac{k}{m}}$

where $k$ is spring constant and $m$ is the mass of object

so for the given mass $m_{2}$ , angular frequency will be

$ω = \sqrt{\frac{k}{m_{2}}}$

Now for amplitude, we know the formula

$y = A s i n ω t$

here $t$ is the time period, A is amplitude and $ω$ is angular frequency

Putting the value of $ω$ here

$y = A s i n (\sqrt{\frac{k}{m_{2}}}) t$

Suggest Corrections

Similar questions

Q. Two masses

m_{1}

and

m_{2}

are suspended together by a massless spring of constant K as shown in figure. When the masses are in equilibrium,

m_{1}

is removed without disturbing the system. Find the angular frequency and amplitude of oscillation of

m_{2}

Two masses $m_{1}$ and $m_{2}$ are suspended together by a massless spring of constant k. When the masses are in equilibrium, $m_{1}$ is removed without disturbing the system. Then the angular frequency of oscillation of $m_{2}$ is

Q. Two masses

m_{1}

and

m_{2}

are suspended from a massless spring of force constant K. When the masses are in equilibrium,

m_{1}

is removed without disturbing the system. The angular frequency and amplitude of oscillation is

Q. Two masses

m_{1} = 1 k g

and

m_{2} = 0.5 k g

are suspended together by a massless spring of spring constant

12.5 N m^{- 1}

. When masses are in equilibrium

m_{1}

is removed without disturbing the system. New amplitude of oscillation will be

Q. Two masses

m_{1}

and

m_{2}

are suspended together by a massless spring of spring constant

k

. When the masses are in equilibrium,

m_{2}

is removed without disturbing the system. The amplitude of SHM is

Join BYJU'S Learning Program

Two masses m1 and m2 are suspended together by a massless spring of spring constant k (Fig). When the masses are in equilibrium, m1 is removed without disturbing the system. Find the angular frequency and amplitude of oscillation of m2.

Two masses $m_{1}$ and $m_{2}$ are suspended together by a massless spring of spring constant $k$ (Fig). When the masses are in equilibrium, $m_{1}$ is removed without disturbing the system. Find the angular frequency and amplitude of oscillation of $m_{2}$ .