Question

The vertical motion of mass a is defined by the relation x = cos(10t) – 0.1sin(10t), where x and t are expressed in mm and seconds, respectively. Consider t = 0.35 s. What is the value of x at t = 0.35 s?

Answer 1

To find the value of x at t = 0.35 s, plug in the value of t into the equation x = cos(10t) - 0.1sin(10t), then calculate the cosine and sine values for 3.5, and combine them to get x.

Step-by-step explanation:

To calculate the value of x at t = 0.35 s for the vertical motion of a mass provided by the relation x = cos(10t) − 0.1sin(10t), we substitute the given value of t into the equation.

1. First, we find the cosine and sine values for 10t, where t = 0.35 s, so 10t = 3.5.
2. Then, we calculate cos(3.5) and −0.1sin(3.5).
3. After finding these values, we add them to get the value of x.

Let's perform the calculation:

x = cos(3.5) − 0.1sin(3.5)

Note: To find the exact numerical value, we would use a calculator to evaluate the trigonometric functions. The student should do this as the final step to get the answer.