QuestionMay 21, 2025

2. A small block is attached to an ideal spring and is moving in SHM on a horizontal,frictionless surface . When the amplitude of the motion is 0.090 m , it takes the block 2.70 s to travel from to . If the amplitude is doubled, to , how long does it take the block to travel (a ) from to and (b) from to ?

2. A small block is attached to an ideal spring and is moving in SHM on a horizontal,frictionless surface . When the amplitude of the motion is 0.090 m , it takes the block 2.70 s to travel from to . If the amplitude is doubled, to , how long does it take the block to travel (a ) from to and (b) from to ?
2. A small block is attached to an ideal spring and is moving in
SHM on a horizontal,frictionless surface . When the amplitude
of the motion is 0.090 m , it takes the block 2.70 s to travel from
to . If the amplitude is doubled, to , how long does it take the
block to travel (a ) from to and (b) from to ?

Solution
4.2(238 votes)

Answer

(a) 2.70 s; (b) 1.35 s Explanation 1. Determine the period of SHM The time to travel from one end to the other is half the period. Given time for half-period is 2.70 s, so the full period T = 2 \times 2.70 = 5.40 s. 2. Calculate new period with doubled amplitude Period T in SHM is independent of amplitude. Thus, even if amplitude doubles, T remains 5.40 s. 3. Calculate time for (a) from one end to the other Time for half-period remains unchanged at 2.70 s. 4. Calculate time for (b) from one end to the equilibrium position Time for quarter-period is \frac{T}{4} = \frac{5.40}{4} = 1.35 s.

Explanation

1. Determine the period of SHM<br /> The time to travel from one end to the other is half the period. Given time for half-period is 2.70 s, so the full period $T = 2 \times 2.70 = 5.40$ s.<br /><br />2. Calculate new period with doubled amplitude<br /> Period $T$ in SHM is independent of amplitude. Thus, even if amplitude doubles, $T$ remains 5.40 s.<br /><br />3. Calculate time for (a) from one end to the other<br /> Time for half-period remains unchanged at 2.70 s.<br /><br />4. Calculate time for (b) from one end to the equilibrium position<br /> Time for quarter-period is $\frac{T}{4} = \frac{5.40}{4} = 1.35$ s.
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