Question

An object of mass $0.4\text{kg}$, hanging from a spring with a spring constant of,$8.0\text{N/m}$ is set into an up-and down simple harmonic motion. What is the magnitude of the acceleration of the object when it is at its maximum displacement of $0.10\text{m}$? (a)Zero (b)$0.45{\text{m/s}}^{\text{2}}$ (c)$1.0{\text{m/s}}^{\text{2}}$ (d)$2.0{\text{m/s}}^{\text{2}}$(e)$2.4{\text{m/s}}^{\text{2}}$.

Short answer

Option (d) is correct. The acceleration of the object when it is at its maximum displacement of$0.10m$ is$a=2.0{\text{m/s}}^{\text{2}}$

Step-by-step solution

Step 1: The total energy of a simple harmonic oscillator

The total energy of a simple harmonic oscillator is a constant of the motion and is given by

$E=\frac{1}{2}k{A}^2$

$E=$Total energy

$L=$Length of pendulum

$K=$Constant

Step 2: Find the magnitude of the acceleration of the object

When the object is at its maximum displacement, the magnitude of the force exerted on it by the spring is . $F_s=K\left|X_{\max }\right|=\left(8\text{N/m}\right)\left(0.10\text{m}\right)=0.80\text{N}$This force will give the mass an acceleration of

$$\begin{gathered} \backslash \mathrm{begingathered}a=\frac{F_s}{m}=\frac{0.80\text{N}}{0.40\text{kg}}\backslash \mathrm{hfill} \\ a=2.0{\text{m/s}}^{\text{2}}\backslash \mathrm{hfill} \\ \backslash \mathrm{endgathered} \end{gathered}$$uncaught exception: Http Error #502

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Option (d) is correct. The acceleration of the object when it is at its maximum displacement of$0.10m$ is$a=2.0{\text{m/s}}^{\text{2}}$