InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
What is meant by angular harmonic oscillations? Compute the time period of angular harmonic oscillation. Time period and frequency of angular SHM: |
| Answer» <html><body><p></p>Solution :(i) When a body is allowed to rotate freely about a given axis then the oscillation is known as the angular oscillation. <br/> (ii) The point at which the resultant torque acting on the body is taken to be zero is called mean position . If the body is displaced from the mean position , then the resultant torque <a href="https://interviewquestions.tuteehub.com/tag/acts-848461" style="font-weight:bold;" target="_blank" title="Click to know more about ACTS">ACTS</a> such that it is proportional to the angular displacement and this torque has a tendency to bring the body towards the mean position. <br/> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/SUR_PHY_XI_V02_C10_E03_003_S01.png" width="80%"/> <br/> (iii) <a href="https://interviewquestions.tuteehub.com/tag/let-11597" style="font-weight:bold;" target="_blank" title="Click to know more about LET">LET</a> `vec(theta)` be the angular displacement of the body and the resultant torque `vec(tau)` acting on the body is<br/> `vec(tau)propvec(theta)""...(i)`<br/> `vec(tau)=-kvec(theta)""...(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)` <br/> k is the <a href="https://interviewquestions.tuteehub.com/tag/restoring-1187260" style="font-weight:bold;" target="_blank" title="Click to know more about RESTORING">RESTORING</a> torsion constant , which is torque per unit angular displacement . If I is the moment of inertia of the body and `vec(alpha)` is the angular acceleration then <br/> `vec(tau)=Ivec(alpha)=-kvec(theta)`<br/> But, `vec(alpha)=(d^(2)vec(theta))/(dt^(2))`<br/> `vec(alpha)=(d^(2)vec(theta))/(dt^(2))=-(K)/(I)vec(theta)""...(3)` <br/> `vec(alpha)=omega^(2) theta""...(4)`<br/> (iv) This differential equation resembles simple harmonic differential equation . So, comparing equation (3) & (4) we get <br/> `omega=sqrt((K)/(I) )"rad"s^(-1)""...(4)`<br/> (v) This frequency of the angular harmonic motion is<br/> `f=(1)/(2pi)sqrt((K)/(I))HZ""....(5)`<br/> (vi) The time period is<br/> `T=2pisqrt((I)/(K))" second"....(<a href="https://interviewquestions.tuteehub.com/tag/6-327005" style="font-weight:bold;" target="_blank" title="Click to know more about 6">6</a>)`</body></html> | |