A mass is attached to the end of a spring and set into...

A mass is attached to the end of a spring and set into oscillation on a horizontal frictionless surface by releasing it from a stretched position. The position of the mass at any time is described by x = (8.8 cm)cos[2πt/(2.68 s)]. Determine the following. (a) period of the motion (s) (b) frequency of the oscillations (Hz) (c) first time the mass is at the position x = 0 (s) (d) first time the mass is at the site of maximum compression of the spring

Transcript

00:01 Hello students, so in this question we are given that a mass is attached to the end of a spring and it is set into oscillation on a horizontal frictionless surface by releasing it from a stretched position.

00:11 And we are given the equation of motion as y equals to 8 .8 cost 2 pi t divided by 2 .68 seconds.

00:27 So this is the equation of motion given in the first part we have to calculate the time period of the motion so calculate the time period of the motion we will see that in this equation why is the distance from the origin and 8 point is the amplitude and here 2 pi divided by 2 .68 this whole represents omega and here we have t so the formula for omega is omega is equals to 2 pi divided 2.

00:58 By t where capital t is time period so from this equation we can compare these two values 2 pi divided by 2 .68 so from here we can see that the value of time period will be equal to 2 .68 seconds okay so moving on to the next part in the next part we have to calculate the value of frequency so frequency will be equal to 1 divided by time period that is it is the reciprocal of time period so it is equals to 1 divided by 2 .68 which is equal to 0 .37 heads.

01:32 Okay.

01:33 So moving on to the next part.

01:35 In the next part we have to tell when the first time the mass is at position x equals to 0.

01:42 Okay so let's say this is our spring and this is the mass.

01:50 Let's say this is the equilibrium position.

01:52 We have to tell when it will reach the equilibrium position for the first time.

01:58 So when it will reach the equilibrium position the value of y will be equal to zero.

02:02 So we can equate it 0 equals to cost 2 pi t divided by 2 .68.

02:11 So cost 0, the value of cost theta is equal to 0 only at 90 degree or we can say pi by 2 radiance...

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