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A particle is executing linear SHM. For this match the following :- ( array |c|l|c|l| i & If mass of the block is doubled & (keeping other factor constant) & a & Energy of oscillation becomes 4 times ii & If amplitude of oscillation is doubled & (keeping other factor constant) & b & Max. speed of the particle becomes half times iii & If force constant is doubled & (keeping other factor constant) & c & Time period bec

Options

  1. A( i - c ), ii -a, iii -d, iv -b
  2. Bi -c , ii -a , iii -b , iv -d
  3. Ci (-a ), ii (-c ), iii (-b ), iv (-d )
  4. Di -c , ii -b , iii -d , iv -a

Correct answer

A. ( i - c ), ii -a, iii -d, iv -b

Step-by-step solution

( aligned & Energy E = 1 2 KA ^2= 1 2 mw ^2 ~A ^2 & v _ = A = A K m & T =2 ~m ~K & ( P.E. )_ = 1 2 KA ^2 aligned ) (i) ( ) Mass is doubled ( ) Time period become ( 2 ) times. (ii) ( ) Amplitude ( ) double Energy ( 4 ) times ( v _ 2 ) times (P.E.) ( _ 4 ) times (iii) ( K ) double Energy = double ( v _ max = 2 ) times ( T 1 2 ) times (P.E.) ( _ max =2 ) times (iv) Angular frequency ( ( = k m ) ) is halfed means k becomes (1 / 4 ) times so maximum speed is halfed.

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