An object executes periodic motion which is given by $$sin4$$$$π$$t−$$cos$$ $$4$$$$π$$t. Then we can say that

Question

An object executes periodic motion which is given by $$sin4$$$$π$$t−$$cos$$  $$4$$$$π$$t.  Then we can  say that

Infinity Learn · Accepted Answer

The function $$sin4$$$$π$$t−$$cos$$  $$4$$$$π$$t will represent a periodic motion, if it is identically  repeated after a fixed interval of time. If this is also a simple harmonic motion.  Then we can uniquely write that as  Asinω $$t+$$ϕ ∴$$sin4$$$$π$$t−cas  $$4$$$$π$$t  can be reduced as $$follows212sin4$$$$π$$t−$$12cos$$  $$4$$$$π$$t (multiplying$$ & dividing by $$2$$ $$)=2cos$$$$π$$$$4sin(4$$$$π$$$$t)−$$sin$$$$π$$$$4cos$$  (4$$$$π$$$$t)∵$$sin$$$$π$$$$4=$$$$cos$$$$π$$$$4=12$$    The above relation can be written $$as=2sin$$π  t−π$$4$$∵sinAcosB−$$cosAsinB=$$$$sin$$(A$$−$$B) The above equation can be compared with  $$y=Asin($$ω $$t+$$ϕ$$)$$ This show that the  function $$sin$$(4$$$$π$$t−$$cos$$  $$4$$$$π$$$$t) is simple harmonic with its resultant as  $$2sin$$π  t−π$$4$$.  Its time period can be found using ω$$=2$$$$π$$T Here ω$$=4$$π,ω$$=4$$$$π$$$$2$$$$π$$$$T=4$$$$π$$$$T=12s$$

An object executes periodic motion which is given by $\sin 4 π t - c o s 4 π t .$ Then we can say that

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An object executes periodic motion which is given by sin4πt−cos 4πt. Then we can say that

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An object executes periodic motion which is given by $\sin 4 π t - c o s 4 π t .$ Then we can say that