A particle of mass 10 g moves in a field where the potential energy per unit mass is U = 8 × 1 0 4 x 2 erg/g. If the total energy of the particle is 8 × 1 0 7 erg, the relation between x and time t is ( ϕ = constant):

U = 2 1 ω 2 x 2 ⋅ (per unit mass)= 8 × 1 0 4 x 2 gives ω 2 = 1.6 × 1 0 5 , so ω = 400 rad/s. E = 2 1 m ω 2 A 2 = 8 × 1 0 7 with m = 10 g gives A 2 = 100 cm², so A = 10 cm.

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A particle of mass 10 g moves in a field where the potential energy per unit mass is $U = 8 \times 1 0^{4} x^{2}$ erg/g. If the total energy of the particle is $8 \times 1 0^{7}$ erg, the relation between $x$ and time $t$ is ( $ϕ$ = constant):

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Solution:

$U = \frac{1}{2} ω^{2} x^{2} \cdot$ (per unit mass)= $8 \times 1 0^{4} x^{2}$ gives $ω^{2} = 1.6 \times 1 0^{5}$ , so $ω = 400$ rad/s. $E = \frac{1}{2} m ω^{2} A^{2} = 8 \times 1 0^{7}$ with $m = 10$ g gives $A^{2} = 100$ cm², so $A = 10$ cm.

Subject:PhysicsTopic:SHMSubtopic:Oscillations and SHM

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