4. A block-spring oscillator exhibits simple harmonic motion with an amplitude A and its maximum speed is vmar (a) Write a mathematical expression for the total energy of an oscillator in terms of its angular frequency, w, mass (m), and its amplitude A. (b) Write a mathematical expression for the total energy of an oscillator in terms of its position (r), mass (m), spring constant (k) and speed (v). 1 (c) When the block's speed is maz, Sshow that the distance (rm) from the central equilib- rium position is: 3mw2 A? Im = V 4k
4. A block-spring oscillator exhibits simple harmonic motion with an amplitude A and its maximum speed is vmar (a) Write a mathematical expression for the total energy of an oscillator in terms of its angular frequency, w, mass (m), and its amplitude A. (b) Write a mathematical expression for the total energy of an oscillator in terms of its position (r), mass (m), spring constant (k) and speed (v). 1 (c) When the block's speed is maz, Sshow that the distance (rm) from the central equilib- rium position is: 3mw2 A? Im = V 4k
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Transcribed Image Text:4. A block-spring oscillator exhibits simple harmonic motion with an amplitude A and its
maximum speed is vmar-
(a) Write a mathematical expression for the total energy of an oscillator in terms of its
angular frequency, w, mass (m), and its amplitude A.
(b) Write a mathematical expression for the total energy of an oscillator in terms of its
position (r), mass (m), spring constant (k) and speed (v).
1
(c) When the block's speed is Umaz; Sshow that the distance (Im) from the central equilib-
rium position is:
3mw²A²
Im
4k
(d) When the block's position is A, show its speed (v) is given by:
kA?
v = /w²A?
4m
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