21Hint: use trigonometric identities..
1. The displacement y of a particle executing periodic motion is given by y = 4 cos2(t/2) sin (1000t).
The above expression may be considered to be a result of superposition of how many waves?
A) 2 B) 3 C) 4 D) 5
2. A function x = A sin2ωt + B cos2ωt + C cos ωt sin ωt represents SHM when :-
A) for all A,B,C (C≠0)
B) A = -B , C=2B ≠0
C) A = B , C = 0
D) A = B , C = 2B ≠0
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14 Answers
49Acos2at sinbt = A2(cos2at + 1)sinbt = A2cos2at.sinbt + A2sinbt
sin(2at+bt)= sinbtcos2at + sin2atcosbt
sin(bt-2at) = sinbtcos2at - sin2atcosbt
sinbt.cos2at = 12[sin(bt+2at)+sin(bt-2at)]
so f(t) = A4sin(bt+2at) + A4sin(bt-2at) + A2sinbt
3 SHMs!! :)
71@Subho Bhaiya.
Sorry Answer Doesn't matches!. (One answer i could clearly figure out but one is not coming) i.e., DON't SEE -> There are two answers)
713. A Piston of cross section area A is fitted in cylinder in which gas of Volume " V " and at pressure " P " is enclosed. What is the angular frequency (the piston is displaced slightly) if the gas obeys Boyle's law :-
A) \sqrt{\frac{Ag}{V}}
B) 2\sqrt{\frac{Ag}{V}}
C) \sqrt{\frac{2Ag}{V}}
D) \frac{3Ag}{V}
262Q1) ans- 3
Q2) ans A (try using trigo and then if A=B then C≠0)
1062. The most general solution is A+B equals 0 and C can have any value .
U can obtain this by applying defn of shm ie
double derivative of x equals -w squared x where w is freq of shm (here it is 2w)
492) oops.. i shud have got B, D!
B-->
f(t)=Bsin2wt+Bcos2wt = √2Bsin(wt+pi/4)
106m sorry . The answer will be
shm for A,B,C except one particular case: A equals B ,and C equals 0.
All oder values of A,B,C represent shm
493) PA=mg
P'(V-Ax)=PV
P'=PVV-Ax
|F|=P'A-PA = (P'-P).A=PAAxV-Ax=mg.AxV-Ax = mg.AxV (approx.)
Vectorially,
F = -mgAV.x
a = -AgV.x
w2 = AgV`
49@Asish: If option c was not given I wud have also said A! ;)