Question

A student observes that the motion of a weight oscillating up and down on a spring can be modeled by the following equation, where h is the weight's height above the ground, in meters, and t is the time, in seconds.

h(t)=0.5 x sin(πt+π/2)+1

On the graph, plot the points where height, h(t), is at a maximum.

Answer 1

See image below

Explanation:

Answer 2

the height will be maximum at 1.5

Explanation:

We have been given the function:

`h(t)=0.5\cdot sin(\pi t+(\pi)/(2))+1`

Height depends on
`(sin(\pi t+(\pi)/(2))`

`(sin(\pi t+(\pi)/(2))`

This will be maximum when value of its is 1

And value will be 1 when t=0.

So, substitute the value of t=0 in given function:

`h(0)=0.5\cdot sin(\pi 0+(\pi)/(2))+1`

`h(0)=0.5\cdot sin((\pi)/(2))+1`

`\Rightarrow h(0)=0.5(1)+1`

`h(t)=1.5`

Hence, the height will be maximum at 1.5