14 it takes 20 n of force to stretch a spring 5 cm from...

Name: 14 it takes 20 n of force to stretch a spring 5 cm from equilibrium a mass of 4 g is suspended from the spring initially at rest in equilibrium and is let go find xt the displacement from eq 15058
Uploaded: 2022-04-16T15:24:44-08:00
Duration: 9 min 52 s
Channel: Shyam P
Description: 14 it takes 20 n of force to stretch a spring 5 cm from equilibrium a mass of 4 g is suspended from the spring initially at rest in equilibrium and is let go find xt the displacement from eq 15058

14. It takes 20 N of force to stretch a spring 5 cm from equilibrium. A mass of 4 g is suspended from the spring initially at rest in equilibrium and is let go. Find 𝑥(𝑡) – the displacement from equilibrium at 3me t as a single sine func3on. Leave all quantaties exact.

Transcript

00:01 Hello everyone here the problem is given that in this problem we have given that mass m is equal to 3k z and l is equal to 0 .6 meter and force is equal to 20 newton from hoax law f is equal to kx f is equal to kx here the value of f is 20 newton is equal to k and the values of x is here the length is l is 0 .6 so this is the x then the values of x is 0 .6 so the value of x is equal to 20 divided by 0 .6 this is equal to 200 divided by 6 this can be written as this so there is no denying so damping coefficient is damping coefficient is equal damping coefficient is c is equal to 0 and the differential equation is given by so the differential equation differential equation is given by my derivative plus cy dash plus ky is equal to 0 the value of m is 3k z so this is 3y dash plus the value of c is the value of c is 0 then we put here 0 y dash plus the value of k is 200 divided by 6 y is equal to 0 so 3y double dash this is plus 200 divided by 6 into y this is equal to 0 this can be written as 3x 2 plus 200 divided by 6 is equal to 0.

02:35 The value of x squared 3x square is equal to the value of 3x square is equal to minus 200 divided by 6 and the value of x square is equal to and the value of x square is equal to minus 200 divided by 6 into 3.

02:58 After we divided by 2, 2 3 is 6 and 200 2 into 100 is 200.

03:04 So this is x squared, the value of x square is equal to minus hundred divided by three and the value of x is equal to under root of minus hundred divided by nine.

03:20 Then x is equal to plus minus here is 10 and the whole square of three is nine.

03:28 So here is three.

03:29 Then the values of x is plus minus three aorta.

03:34 Okay.

03:36 For complex root, the general solution is for, complex roots...