Answer:
a) t=24s
b) number of oscillations= 11
Explanation:
In case of a damped simple harmonic oscillator the equation of motion is
m(d²x/dt²)+b(dx/dt)+kx=0
Therefore on solving the above differential equation we get,
x(t)=A₀
where A(t)=A₀
A₀ is the amplitude at t=0 and
is the angular frequency of damped SHM, which is given by,

Now coming to the problem,
Given: m=1.2 kg
k=9.8 N/m
b=210 g/s= 0.21 kg/s
A₀=13 cm
a) A(t)=A₀/8
⇒A₀
=A₀/8
⇒
applying logarithm on both sides
⇒
⇒
substituting the values

b) 

, where
is time period of damped SHM
⇒
let
be number of oscillations made
then, 
⇒
<h2>
Answer:</h2>
1000th multiple of the standard reference level for intensities.
<h2>
Explanation:</h2>
The sound intensity level (β), measured in decibels, of a sound with an intensity of I is defined as follows;
β = 10 log (I / I₀) --------------------(i)
Where;
I₀ = reference intensity
Given from the question;
β = sound level = 30dB
Substitute this value into equation (i) as follows;
30 = 10 log (I / I₀)
Divide both sides by 3;
3 = log (I / I₀)
Take antilog of both sides;
10^(3) = (I / I₀)
1000 = I / I₀
Solve for I;
I = 1000I₀
Therefore the intensity of the sound is 1000 times the standard reference level for intensities (I₀)
Answer with Explanation:
We are given that
Weight of an ore sample=17.5 N
Tension in the cord=11.2 N
We have to find the total volume and the density of the sample.
We know that
Tension, T=
=buoyancy force
T=Tension force
W=Weight
By using the formula

N

Where
=Volume of object
=Density of water
=Acceleration due to gravity
Substitute the values then we get


Volume of sample=
Density of sample,
Where mass of ore sample=1.79 kg
Substitute the values then, we get

Density of the sample=
Answer:
the reason for the acceleration month that the coefficient of kinetic friction is less than the coefficient of satic frictionExplanation:
This exercise uses Newton's second law with the condition that the acceleration is zero, by the time the body begins to slide. At this point the balance of forces is
fr- w || = 0
The expression for friction force is that it is proportional to the coefficient of friction by normal.
fr = μ N
When the system is immobile, the coefficient of friction is called static coefficient and has a value, this is due to the union between the surface, when the movement begins some joints are broken giving rise to coefficient of kinetic friction less than static.
In consequence a lower friction force, which is why the system comes out of balance and begins to accelerate.
μ kinetic <μ static
In all this movement the normal with changed that the angle of the table remains fixed.
Consequently, the reason for the acceleration month that the coefficient of kinetic friction is less than the coefficient of satic friction
Answer:
The bullet that is fired will spend longer in the air, hitting the ground after the dropped bullet.
Explanation:
Using the equation: x
= x
0 +
v
t
If we neglect the effects of air resistance, the horizontal motion is a constant velocity.
The horizontal displacement = (velocity X cosθ)
So, the fired bullet has to travel horizontally before falling which takes a longer time compared to a bullet dropped where it is, height = 1/2 gt^2
gravity, g = 9.8 m/s2.