Question

1 point) A mass is hung from a spring and set in motion so that it oscillates continually up and down. The velocity v of the weight at time t is given by the equation v=−4.5cos(3.5πt) with v measured in feet per second and t measured in seconds. Determine the maximum velocity of the mass and the amount of time it takes for the mass to move from its lowest position to its highest position. Maximum velocity = Time from low to high = ;

Answer 1

to find the maximum velocity of the mass and the time it takes to move from its lowest position to its highest position, you can use the equation for velocity:

v = -4.5 cos(3.5πt)

1. maximum velocity:
the maximum velocity occurs when the cosine function has a value of -1 (at the bottom of its oscillation). therefore, the maximum velocity is:

v_max = 4.5 feet per second.

2. time from low to high:
to find the time it takes for the mass to move from its lowest position to its highest position, you need to determine the time it takes for the cosine function to go from -1 (lowest) to 1 (highest).

the cosine function completes one full cycle from -1 to 1 every 2π radians. in your equation, you have 3.5πt, so it will take:

time from low to high = (2π) / 3.5π = 2/3.5 seconds.

now, you can calculate this:

time from low to high ≈ 0.571 seconds.

so, the maximum velocity is 4.5 feet per second, and it takes approximately 0.571 seconds for the mass to move from its lowest position to its highest position.