A particle executes SHM along $$x-axis$$ with a frequency $$25$$$$π$$Hz. The mass of the particle is $$0.20$$ kg. At the position x $$=$$ $$0.04$$ m, the kinetic energy is $$0.50$$ J and the potential energy is $$0.40$$ J. The potential energy is zero at mean position. The amplitude of oscillations (in$$ $$cm) is $$__________$$.

Question

A particle executes SHM along $$x-axis$$ with a frequency $$25$$$$π$$Hz. The mass of the particle is $$0.20$$ kg. At the position x $$=$$ $$0.04$$ m, the kinetic energy is $$0.50$$ J and the potential energy is $$0.40$$ J. The potential energy is zero at mean position. The amplitude of oscillations (in$$ $$cm) is $$__________$$.

Infinity Learn · Accepted Answer

$$K=(2$$$$π$$$$f)2mEnergy$$ of oscillations $$=$$ $$0.9$$ $$J0.90=12KA2A=1.84$$$$π$$$$2f2m1/2=12$$$$π$$$$f1.80.21/2=6cm$$

Simple harmonic motion

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$K = (2 π f)^{2} m$
Energy of oscillations = 0.9 J
$\begin{array}{l} 0.90 = \frac{1}{2} K A^{2} \\ A = {[\frac{1.8}{4 π^{2} f^{2} m}]}^{1 / 2} = \frac{1}{2 π f} {[\frac{1.8}{0.2}]}^{1 / 2} = 6 cm \end{array}$

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Simple harmonic motion

Remember concepts with our Masterclasses.

A particle executes SHM along x-axis with a frequency 25πHz. The mass of the particle is 0.20 kg. At the position x = 0.04 m, the kinetic energy is 0.50 J and the potential energy is 0.40 J. The potential energy is zero at mean position. The amplitude of oscillations (in cm) is __________.

K=(2πf)2mEnergy of oscillations = 0.9 J0.90=12KA2A=1.84π2f2m1/2=12πf1.80.21/2=6cm

Ready to Test Your Skills?

free study material

$K = (2 π f)^{2} m$
Energy of oscillations = 0.9 J
$\begin{array}{l} 0.90 = \frac{1}{2} K A^{2} \\ A = {[\frac{1.8}{4 π^{2} f^{2} m}]}^{1 / 2} = \frac{1}{2 π f} {[\frac{1.8}{0.2}]}^{1 / 2} = 6 cm \end{array}$