Question

a weight is attached to a spring and reaches its equilibrium position (x = 0). it is then set in motion resulting in a displacement of x = 10 cos t, where x is measured in centimeters and t is measured in seconds. see the figure shown to the right. answer parts (a) and (b). (a) what is the springs displacement when t = 0? 10 cm (type an integer or decimal rounded to one decimal place as needed.) what is the springs displacement when t = $\frac{pi}{3}$? cm (type an integer or decimal rounded to one decimal place as needed.)

Explanation:

Step1: Substitute t value

We are given the displacement formula $x = 10\cos t$. To find the displacement when $t=\frac{\pi}{3}$, we substitute $t = \frac{\pi}{3}$ into the formula.

Step2: Calculate cosine value

We know that $\cos\frac{\pi}{3}=\frac{1}{2}$. So $x = 10\times\cos\frac{\pi}{3}=10\times\frac{1}{2}$.

Step3: Get the result

$x = 5$ cm.

Answer:

5 cm