Q1) Find the output y(t) of an LTI system with impulse...

Q1) Find the output $y(t)$ of an LTI system with impulse response $h(t)$ when driven by the input $x(t)$ in each of the following cases: a) $h(t) = sinc(t)$ $x(t) = cos(2\pi f_0 t)$ b) $h(t) = sinc(t)$ $x(t) = sinc(t)$ c) $h(t) = \delta(t) + \delta'(t)$ $x(t) = e^{-\alpha |t|}, (\alpha > 0)$ d) $h(t) = e^{-\alpha t}u(t)$ $x(t) = e^{-\beta t}u(t) \quad (\alpha, \beta > 0)$ where $u(t)$ is the unit step function, $\delta'(t) = \frac{d\delta(t)}{dt}$, and $sinc(t) = \frac{sin(\pi t)}{\pi t}$.

Transcript

00:01 We are given here a group of students observed that wooden block we are given a wooden block of mass and which is equal to 0 .40 kilogram and of the string and the radius we are given here are which is equal to 0 .7 meter and it makes 9 rotation in 20 seconds so we can write number of rotation is 9 rotations so 9 rotations and we can write the time we are given here is 20 .7 seconds and when in this event will and when what is the block tenetial linear speed we want to find this block speed or we can say tenderness speed we want to find vt we want to find and also it is block angular speed we want to find the block angular speed so let's find out so we know the radius we are given here mass we are given here so first we can write the parameter of the circle so we can write here parameter so parameter which is equal to we know that is all circumference we are can also see circumference now we can write substitute value into this formula so you can write 2 multiply by 3 .14 multiplied by value of r is 0 .7 now we are simply for all this value can write here 4 .4 meter answer is 4 .4 meter now here let's find out total distance travel so we can write total distance x which is equal to we can write the velocity here we know that xbis equal we can write 9 rotation multiple by we know there is this parameter which is equal to we can write distance table is we just substitute this value and we just multiply this to value and we can write your answer is 39 .t 8 meters so this is the value of x now let's find out total time taken so time which is equal we know that it is time taken is 20 .7 second so here time taken is 20 .7 second so let's find out linear speed so we know the tenderness speed which is equal to x divided by time t we know the x which is equal to 39 .58 divided by we can write 20 .1 which is equal to we can write your answer is 1 .91 meter per second so this is the value of vt tangentous speed.

02:16 Now let's find out the part b in the second question...

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