Question

37. /m, is A kg mass attached to a massless spring with spring constant k-38 N oscillating without friction. If the mass has a velocity of 2.1 m/s when it is at the equilibrium position, what is the amplitude of the oscillation? b. 0.19 m c. 0.25 m d. 0.33 m e. 0.42 m 38. On earth, you have a pendulum of length L that oscillates with period T. Your friend lives on a planet where the acceleration of gravity is twice as big as it is on the earth. What should be the length of a pendulum on your friend's planet so that it also oscillates with the same period T? a. L b. 2L c. 4L 39. A string is stretched between two fixed posts a distance L apart. What is the maximum wavelength for standing waves on this string? a. L b. L/2 c. 2L Page 15 of 16 (42 problems)

Answer 1

37)

max velocity is given by

v = wA

where'w = sqrt (k/m) = sqrt (38/1.5) = 5.0333 rad/sec

so,

A = v/w

A = 2.1 / 5.0333

A = 0.417 m

option (e) looks okay

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38)

We know

T = 2 $\pi$ sqrt (L/g)

or

after squaring both sides,

L_earth = T²g / 4 $\pi$ ² ------------- (1)

Now, on other planet g = 2g

so,

L_planet = T² . 2g / 4 $\pi$ ² ------- (2)

compare (1) and (2)

L_planet = 2*L_earth

so, option b is fine

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39) maximum wavelength is L only