Answer:

Explanation:
The attached image shows the system expressed in the question.
We can define an expression for the system.
The equivalent equation for the system would be

so, the input signal could be expressed in dB terms
(1)
so the output signal could be expressed as.

The gain should be expressed in dB terms and power in dBm terms so

using the (1) equation to find it in terms of Watts

The spring constant is 66.7 N/m
Explanation:
First of all, we have to find the magnitude of the force acting on the spring. This is equal to the weight of the mass hanging on the spring, which is:

where:
m = 0.50 kg is the mass of the object
is the acceleration of gravity
Substituting,

Now we can use Hookes' law to find the constant of the spring:

where
F is the force applied
k is the spring constant
x is the stretching of the spring
Here we have:
F = 5 N
While the stretching is
x = 0.075 m
Therefore, ignoring the negative sign in the formula (which only tells us the direction), we find the spring constant:

#LearnwithBrainly
Complete Question
A small object moves along the x-axis with acceleration ax(t) = −(0.0320m/s3)(15.0s−t)−(0.0320m/s3)(15.0s−t). At t = 0 the object is at x = -14.0 m and has velocity v0x = 7.10 m/s. What is the x-coordinate of the object when t = 10.0 s?
Answer:
The position of the object at t = 10s is 
Explanation:
From the question we are told that
The acceleration along the x axis is 
The position of the object at t = 0 is x = -14.0 m
The velocity at t = 0 s is 
Generally from the equation for acceleration along x axis we have that

=> 
=> ![V_{x} = -0.032 [15t - \frac{t^2 }{2} ]+ K_1](https://tex.z-dn.net/?f=V_%7Bx%7D%20%3D%20-0.032%20%5B15t%20-%20%5Cfrac%7Bt%5E2%20%7D%7B2%7D%20%5D%2B%20K_1)
At t =0 s and 
=> ![7.10 = -0.032 [15(0) - \frac{(0)^2 }{2} ]+ K_1](https://tex.z-dn.net/?f=7.10%20%20%3D%20-0.032%20%5B15%280%29%20-%20%5Cfrac%7B%280%29%5E2%20%7D%7B2%7D%20%5D%2B%20K_1)
=>
So
![\frac{dX}{dt} = -0.032 [15t - \frac{t^2 }{2} ]+ K_1](https://tex.z-dn.net/?f=%5Cfrac%7BdX%7D%7Bdt%7D%20%20%3D%20-0.032%20%5B15t%20-%20%5Cfrac%7Bt%5E2%20%7D%7B2%7D%20%5D%2B%20K_1)
=> ![\int\limits dX = \int\limits [-0.032 [15t - \frac{t^2 }{2} ]+ K_1] }{dt}](https://tex.z-dn.net/?f=%5Cint%5Climits%20dX%20%20%3D%20%5Cint%5Climits%20%5B-0.032%20%5B15t%20-%20%5Cfrac%7Bt%5E2%20%7D%7B2%7D%20%5D%2B%20K_1%5D%20%7D%7Bdt%7D)
=> ![X = -0.032 [ 15\frac{t^2}{2} - \frac{t^3 }{6} ]+ K_1t +K_2](https://tex.z-dn.net/?f=X%20%20%3D%20%20-0.032%20%5B%2015%5Cfrac%7Bt%5E2%7D%7B2%7D%20%20-%20%5Cfrac%7Bt%5E3%20%7D%7B6%7D%20%5D%2B%20K_1t%20%2BK_2)
At t =0 s and x = -14.0 m
![-14 = -0.032 [ 15\frac{0^2}{2} - \frac{0^3 }{6} ]+ K_1(0) +K_2](https://tex.z-dn.net/?f=-14%20%20%3D%20%20-0.032%20%5B%2015%5Cfrac%7B0%5E2%7D%7B2%7D%20%20-%20%5Cfrac%7B0%5E3%20%7D%7B6%7D%20%5D%2B%20K_1%280%29%20%2BK_2)
=> 
So
![X = -0.032 [ 15\frac{t^2}{2} - \frac{t^3 }{6} ]+ 7.10 t -14](https://tex.z-dn.net/?f=X%20%20%3D%20%20-0.032%20%5B%2015%5Cfrac%7Bt%5E2%7D%7B2%7D%20%20-%20%5Cfrac%7Bt%5E3%20%7D%7B6%7D%20%5D%2B%207.10%20t%20-14)
At t = 10.0 s
![X = -0.032 [ 15\frac{10^2}{2} - \frac{10^3 }{6} ]+ 7.10 (10) -14](https://tex.z-dn.net/?f=X%20%20%3D%20%20-0.032%20%5B%2015%5Cfrac%7B10%5E2%7D%7B2%7D%20%20-%20%5Cfrac%7B10%5E3%20%7D%7B6%7D%20%5D%2B%207.10%20%2810%29%20-14)
=> 
Answer:
0.000109375 m
Explanation:
d = Distance between grating = 0.5 mm
m = Order

Minima relation

For fourth order minima

For second maxima

From the two equations we get

The wavelength is 0.000109375 m