question_answer 24)

A body describes simple harmonic motion with an amplitude of 5 cm and a period of 0.2 s. Find the acceleration and velocity of the body when the displacement is (a) 5 cm, (b) 3 cm, (c) 0 cm.

Answer:

Here, r = 5 cm = 0.05 m ; T = 0.2 s; \[\alpha \] When displacement is y, then acceleration, \[\text{I=}\frac{\text{1}}{\text{2}}\text{m}{{\text{R}}^{\text{2}}}\text{=}\frac{1}{2}\times 10\times {{\left( 0\cdot 15 \right)}^{2}}kg{{m}^{2}}\] velocity, \[\text{T=2 }\!\!\pi\!\!\text{ }\sqrt{\frac{\text{I}}{\text{ }\!\!\alpha\!\!\text{ }}}\] Case (a) When y = 5 cm = \[\alpha =\frac{4{{\pi }^{2}}l}{{{T}^{2}}}=4\times {{\left( \frac{22}{7} \right)}^{2}}\times \frac{1}{2}\times \frac{10\times {{\left( 0\cdot 15 \right)}^{2}}}{{{\left( 1\cdot 5 \right)}^{2}}}\] m \[=1\cdot 97Nm/rad.\] Case (b) When y = 3 cm = \[0\cdot 05\] m \[\cdot \] Case (c) When\[y=0,\,A=-{{(10\pi )}^{2}}\times 0=0\] \[\text{A=-}{{\text{ }\!\!\omega\!\!\text{ }}^{\text{2}}}\text{y}\]