Wave Mechanics Question 568
Question: A body is executing simple harmonic motion. At a displacement x from mean position, its potential energy is $ E _{1}=2J $ and at a displacement y from mean position, its potential energy is $ E _{2}=8J $ . The potential energy E at a displacement (x + y) from mean position is
Options:
A) 10J
B) 14J
C) 18J
D) 4J
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ E _{1}=\frac{1}{2}kx^{2},,E _{2}=\frac{1}{2}ky^{2}, $
$ E=\frac{1}{2}k{{(x+y)}^{2}}=\frac{1}{2}kx^{2}+\frac{1}{2}ky^{2}+kxy $
$ =E _{1}+E _{2}+2\sqrt{E _{1}E _{2}}=2+8+2\sqrt{16}=18J $
BETA
