Problem $2$

The data given below shows the position of a blok in a spribg$-$mass$-$damper system abd the force acting on

it over $5$ seconds. The goal of this problem is to cherk whether this dath ls realstic of not.

One law that any physicil system follows is the law of cowervation of eneryy. In the ficld of rigid$-$body

dynamies, this law is transformed into work$-$energy theorem, which states that the work done oe a body to

The kinctic energy of a body at any time is definod as$.$

$KE(t)-\frac{1}{2}m{x}^2(t)$

While, the small samoust of wok $W$ that occurs over a sanall instance of time it is calculated as

$W=F*dx=F*Edt$

Thus, the work done on the body one the time period, $t_0{t}_1,$ can be calculated as$,$

$W_{t0+t_1}-{\displaystyle \underset{m}{\overset{t_t}{}}}F(t)*2(t)dt$

The work$-$energy thonem for the time period, $t_0{t}_1,$ ean be written as$,$

$K{E}_{p+t}-W_{pta}=0$

where, $K{E}_{pt+t}-KE(t_1)-KE(t_0)$

You can tale the following steps to check whether the mork$-$energy theorm is satisfled for the given data of

bot.

Calculate the velocity of the hody for all time valuss with the acrarray of the centrol difference method

Calculate the work done on the body by solving

$W_{0s}-{\displaystyle \underset{0}{\overset{s}{}}}F(t)*v(t)dt$

usling Simpeot's rule.

Coupute the ehange in kinctic energy of the body using

$K{E}_{05}=K{E}_5-K{E}_0$

apuation. Assume the miss, $m,$ to be $1$ here.

i$.$e$.|K{E}_{05}-W_{05}|{10}^{-2},$ then you can condude that the peesested datin is plysically accurate.

Prist out your conclusion to the terminal screes.