1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
sammy [17]
3 years ago
13

For a damped simple harmonic oscillator, the block has a mass of 1.2 kg and the spring constant is 9.8 N/m. The damping force is

given by -b(dx/dt), where b = 210 g/s. The block is pulled down 13.0 cm and released. (a) Calculate the time required for the amplitude of the resulting oscillations to fall to 1/8 of its initial value. (b) How many oscillations are made by the block in this time?
Physics
1 answer:
ArbitrLikvidat [17]3 years ago
8 0

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)=A₀e^{\frac{-bt}{2m}}cos(w't+\phi)=A(t)cos(w't+\phi)

where A(t)=A₀e^{\frac{-bt}{2m}}

 A₀ is the amplitude at t=0 and

w' is the angular frequency of damped SHM, which is given by,

w'=\sqrt{\frac{k}{m}-\frac{b^{2}}{4m^{2}} }

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

⇒A₀e^{\frac{-bt}{2m}} =A₀/8

⇒e^{\frac{bt}{2m}}=8

applying logarithm on both sides

⇒\frac{bt}{2m}=ln(8)

⇒t=\frac{2m*ln(8)}{b}

substituting the values

t=\frac{2*1.2*ln(8)}{0.21}=24s(approx)

b) w'=\sqrt{\frac{k}{m}-\frac{b^{2}}{4m^{2}} }

w'=\sqrt{\frac{9.8}{1.2}-\frac{0.21^{2}}{4*1.2^{2}}}=2.86s^{-1}

T'=\frac{2\pi}{w'}, where T' is time period of damped SHM

⇒T'=\frac{2\pi}{2.86}=2.2s

let n be number of oscillations made

then, nT'=t

⇒n=\frac{24}{2.2}=11(approx)

You might be interested in
A hammer is used to hit a nail into a board. Which statement is correct about the forces at play between the nail and the hammer
emmasim [6.3K]

Answer:

Hewo My Lovelys!!

Answer is down below!!

Explanation:

The answer is C) The nail exerts an equal force on the hammer in the opposite direction.

Reason: The Newtons third law states that there is an equal an opposite reaction for every action. When hammer pushes the nail, the nail will push the hammer back in opposite direction. When the hammer hits a nail then nail will exert the equal and opposite force to the hammer. These both objects will exert force on each other in opposite directions.

Hope this helps!! =3

Have a great day, evening, of night!! <3

~ XxGhostMosskitxX

5 0
3 years ago
Read 2 more answers
Four balls have the same temperature. Which ball has the most thermal
puteri [66]

Answer:

a bowling ball because it has the most mass.

7 0
3 years ago
Read 2 more answers
A beam of protons enter the electric field of magnitude E = 0.5 N/C between a pair of parallel plates. There is a magnetic field
HACTEHA [7]

Answer:

0.217 m/s

Explanation:

The protons in the beam passes undeflected when the electric force is equal to the magnetic force:

qE = qvB

where

q is the proton's charge

E is the magnitude of the electric field

v is the speed of the protons

B is the magnitude of the magnetic field

Re-arranging the equation,

v=\frac{E}{B}

And by substituting

E = 0.5 N/C

B = 2.3 T

We find

v=\frac{0.5}{2.3}=0.217 m/s

3 0
3 years ago
How do natural actions such as weathering, erosion, and soil formation affect Earth's surface?
zimovet [89]
There are plates under the surface that shift when there is interruption on the surface <span />
8 0
3 years ago
You should be particularly careful a restraining a struggling rabbit because it can
Shtirlitz [24]
You have no options here so I'll just answer. It can cause a rise in heart rate and greatly increases the risk of overheating and even death. If you grab the rabbit too hard, you risk breaking/fracturing a bone or causing other kinds of damage, whether externally or internally, to the rabbit.
6 0
3 years ago
Other questions:
  • A 10.0 kilogram mass of iron on earth exerts a downward force of 98 Newtons. On the moon this same 10.0 kilograms of iron is wei
    9·2 answers
  • A 20000 kg railroad car is rolling at 1.00 m/s when a 1000 kg load of gravel is suddenly dropped in. part a what is the car's sp
    9·1 answer
  • 7) This is a set of equal and opposite forces.
    9·2 answers
  • One deterrent to burglary is to leave your front porch light on all the time. If your local power utility sells energy at 17¢ pe
    13·1 answer
  • What is the number of the lowest energy level that contains an f sublevel?. . 3. . 4. . 5. . 6
    9·1 answer
  • What does critical mean?
    15·2 answers
  • PLS ANSWER FAST WILL GIVE BRAINLEST!!
    10·2 answers
  • NEED IT ASAP!!!!!!!!!!!!!!!!!!!!!
    15·1 answer
  • plss answer what do yo call the substance from the male body that travel to the female body to make children​
    10·2 answers
  • What is the advantage of SI unit over CGS unit?​
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!