Question

An object of mass $0.8kg$ is attached to one end of a spring and the system is set into simple harmonic motion. The displacement x of the object as a function of time is shown in the figure. The magnitude of the object's acceleration at $t=1.0$ is:

• A. Zero
• B. $1.57m/s^2$
• C. $0.197m/s^2$
• D. $0.157m/s^2$

Answer 1

The correct option is C $0.197m/s^2$

From the figure $T=4sec$

$\omega =\frac{2\pi }{T}=\frac{\pi }{2}=1.57rad/sec$

$\Rightarrow \omega =\sqrt{\frac{k}{m}}\Rightarrow k=\left(0.8\right){\left(\begin{array}{c}\frac{\pi }{2}\end{array}\right)}^2$

$=1.97N/m\Rightarrow |a|={\omega }^{2}x=0.197m/s^2$