Question

if differential equation of shm of mass 2g is d2x/dt2+16x=0 then find Force constant
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Answer 1

Given that,

Mass = 2g

The differential equation is

$\dfrac{d^2x}{dx^2}+16x=0$

$\dfrac{d^2x}{dx^2}=-16x$

comparing the general equation

$\dfrac{d^2x}{dx^2}=-\omega^2 x$

$\omega^2=16$

$\dfrac{k}{m}=16$

We need to calculate the force constant

Using formula of restoring force

$F=-kx$

$F+kx=0$

Divided by m on both side

$\dfrac{F}{m}+\dfrac{kx}{m}=0$

$a+\dfrac{kx}{m}=0$

$\dfrac{d^2x}{dx^2}=-\dfrac{k}{m}x$

The force constant is

$\dfrac{k}{m}=16$

$k=16\times2\times10^{-3}$

$k=32\times10^{-3}\ N/m$

Hence, The force constant is $32\times10^{-3}\ N/m$

Learn more :

Topic : differential equation

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Answer 2

Answer:

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