the equation that models the height above or below equilibrium in inches, h, of a spring over time in seconds, t, is h=-30cos(2pi/5 t). at which times will the spring be at a height of 20 in. above equilibrium?

answer options:

1.3 seconds
1.8 seconds
3.2 seconds
4.3 seconds
5.7 seconds

there are 2 correct !

the answers are 1.8 and 3.2 seconds. So both B and C.

Step-by-step explanation:

Option 1 and 3 - 1.3 seconds and 3.2 seconds

Step-by-step explanation:

Given : The equation that models the height above or below equilibrium in inches, h, of a spring over time in seconds, t, is .

To find : At which times will the spring be at a height of 20 in. above equilibrium?        

Solution :

We have given,              

The equation that models the height above or below equilibrium in inches      

We have to find at h=20 inches the time of spring.

We show it graphically,

Plot the graph of the model  

Then, Substitute h=20

The points of their intersections are the solution of the model.

The intersection points are (1.831,20), (3.169,20) and many more.

From the given options,

The time are 1.3 seconds and 3.2 seconds.

Therefore, Option 1 and 3 are correct.    

Refer the attached figure below.  

constant acceleration- a

constant velocity- c

no velocity or acceleration- b

explanation:

for body moving with a constant acceleration, the rate of change of displacement changes over time. this is proven by the increasing gradient of the curve (a) against time.

a body that is moving at constant velocity covers equal distances over equal periods of time, thus the straight line with a constant gradient c.

a stationary body   covers no displacement as time elapses. thus the flat line with   zero gradient.

6/20

step-by-step explanation: