AP EAPCET 25-Aug-2021 Shift 1 Paper

(A) Time-period in spring-block system is given by, T=2π√

m

k

If mass is doubled, T′=2π√

2m

k

⇒ T′=√2T
Hence, time period becomes √2 times, if the mass of the block is doubled.
(A→4)
(B) For spring, PE=

1

2

kx2
If spring constant is increased 4 times, PE becomes 4 times.
(B→3)
(C) Speed of the block, v=ωA Hence, velocity of the block becomes twice when amplitude of the oscillation is doubled.
(C→2)
(D) Energy of the oscillation, E=

1

2

mω2a2
E′=

1

2

mω′2a2
⇒E′=

1

2

m(2ω)2a2=

4

2

mω2a2 (∵)′=2ω)
⇒ E' = 4E
Energy of the oscillation becomes 4 times when angular frequency is doubled.
(D→1)