A particle executes simple harmonic motion according to the displacement equation y $$=$$ $$10$$ $$cos$$$$(2$$$$π$$$$t+$$π$$6)cm$$;, where t is in seconds. The velocity of the particle at t $$=$$ $$16$$ seconds will be:

Question

A particle executes simple harmonic motion according to the displacement equation y $$=$$ $$10$$ $$cos$$$$(2$$$$π$$$$t+$$π$$6)cm$$;, where t is in seconds. The velocity of the particle at t $$=$$ $$16$$ seconds will be:

Infinity Learn · Accepted Answer

Velocity v $$=$$ dydt $$=$$ ddt[$$10$$ $$cos$$(2$$$$π$$$$t+$$π$$6)]                   $$=$$ $$-20$$π $$sin$$(2$$$$π$$$$t+$$π$$6) $$cms-1v(16)$$ $$=$$ $$-20(3.14)$$$$sin$$$$($$π$$3+$$π$$6)cms-1$$    $$=$$ $$62.8$$ cm $$s-1(numerically)$$        [Using $$sin$$ π$$2$$ $$=$$ $$1$$]        $$=$$ $$0.628$$ $$ms-1$$

A particle executes simple harmonic motion according to the displacement equation $y = 10 \cos (2 πt + \frac{π}{6}) cm;$ , where t is in seconds. The velocity of the particle at $t = \frac{1}{6}$ seconds will be:

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A particle executes simple harmonic motion according to the displacement equation y = 10 cos(2πt+π6)cm;, where t is in seconds. The velocity of the particle at t = 16 seconds will be:

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A particle executes simple harmonic motion according to the displacement equation $y = 10 \cos (2 πt + \frac{π}{6}) cm;$ , where t is in seconds. The velocity of the particle at $t = \frac{1}{6}$ seconds will be: