Question

A 2.22 kg mass on a frictionless surface is connected to a wall by a spring of constant 500 N/m. The mass is pulled 10 cm to the right, then released at t = 0. We will describe the motion according to the formula x t   Acos  t  Please answer each of the following questions. a) What are the values of A, , and ? b) What is the maximum velocity of the block? c) What is the acceleration of the block at t = 0.15 s

Answer 1

The description for the given question is described in the explanation section below.

Step-by-step explanation:

`x = A \ cos(wt + phi)`...(equation 1)

`dx/dt = v = - Aw \ sin( wt + phi)`...(equation 2)

at t = 0,

x = 10 &,

v = 0,

From equation 1, we get

⇒
`A = 10 \ cos(phi)`...(equation 3)

⇒
`0 = - 10 w \ sin(phi)`

⇒
`phi=0`

By using this value in equation 3, we get

`A = 10 \ cos(0)`

`A = 10 \ cm`

Now from equation 2, we get

`dv/dt = a = -w \ 2A \ cos(wt)`...(equation 4)

As we know,

`Acceleration = (F)/(m)`

at t = 0,

a = -kA/m

= w2 A

w = root(k/m)

= 15 rad/sec

(b)...

From equation 2, we get

`Vmax = wA`

`=1.5 \ m/sec`

(c)...

From equation 4, we get

`a = - 152* 0.1 cos (15* 0.15)`

`=-14.15 \ m/sec2`