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Grade 10Wave Motion

a)Prove that in simple harmonic motion the average potential energy equals the average kinetic energy when the aver- age is taken with respect to time over one period of the motion, and that each average equals src=data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAD8AAAAmCAIAAAD85NTbAAABmUlEQVRYhe2XXRbEEAyFrSsLsp6sxmaymM4DRRhKk446Z+6bnpZPfm4xx84yqwFE+krvrDHW/Rrlhgp6QjBe+9ETWqRj39h7/ekn5ayJGl/6DfSEYAAprZ1GF3oDfb24hJ4QhieIJjW64MiEw3Nx+rz6xpmcVXPYyawr/GtnUtXVfMEq0M8UalOEcCN/cvp763LxqBPC4HxielY36aDBHTDvC/9Onqyq22SOOaOiZfnQWWNdvkNC0DKn45DTM9qm24XqCpvRU6Ivs3eq+zmLaifhoTi0f4HC2LOS7dWEijFVktGnQ0nf9B8KvYw+R+7gOwtI340129bpV4CUcnqRLhE9a9mUB9ac0WXiy/kT63zDACRqAPDfF9Xmd8QCIKEvzDKafXhUGjsLbi8E+SCDVaZXEfOq6qR/0Smr6UXwDXq1Y+OlGGM+OHfSPfQ0bye/oWeNybs02E6XoqYnBEA3c8NZp5I+2Nkzv0Z1cXpmzpvROxuJA/34PWGNMvr6kvDI2URTDb/fsHKiYhZeHfhj/b9Wpj/9Ou1N/wGaPNS1AHQmRgAAAABJRU5ErkJggg== (b) Prove that when the average is taken with respect to position over one cycle, the average potential energy equals src=data:image/png;base64,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 h and the average kinetic energy equals src=data:image/png;base64,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. (c) Explain physically why the results for (a) and (b) are different.

Profile image of Hrishant Goswami
11 Years agoGrade 10
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2 Answers

Profile image of Navjyot Kalra
11 Years ago
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Profile image of Kushagra Madhukar
6 Years ago
Dear student,
Please find the attached solution to your problem.
 
Wave Motion | 123804 - a)Prove that in simple harmonic motion th ...Wave Motion | 123804 - a)Prove that in simple harmonic motion th ...
Hope it helps.
Thanks and regards,
Kushagra