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). (type an integer or decimal rounded to one decimal place as needed.) what is the springs displacement when t = π/3? 5 cm (type an integer or decimal rounded to one decimal place as needed.) what is the springs displacement when t = 3π/4? cm (type an integer or decimal rounded to one decimal place as needed.)

Explanation:

Step1: Substitute t value

We are given the displacement formula $x = 10\cos t$. Substitute $t=\frac{3\pi}{4}$ into it, so $x = 10\cos(\frac{3\pi}{4})$.

Step2: Evaluate cosine value

We know that $\cos(\frac{3\pi}{4})=-\frac{\sqrt{2}}{2}$. Then $x = 10\times(-\frac{\sqrt{2}}{2})$.

Step3: Calculate x

$x=- 5\sqrt{2}\approx - 7.1$.

Answer:

$-7.1$ cm