The answer choices (a - e), given below, each represent the equation of motion o

Question

The answer choices (a - e), given below, each represent the equation of motion of a particle of mass M travelling on the x axis. Note that in each case, x corresponds to the distance from x = 0 and alpha is a constant. Which one of the equations of motion corresponds to that of a particle executing simple harmonic motion? a. Ma = sigmaF = + alphax i b. Ma = sigmaF = + alphax^-1 i c. Ma = sigmaF = - alphax^2 i d. Ma = sigmaF = - alphax^-1 i e. Ma = sigmaF = - alphax i A small block of mass M is attached to a massless spring having force constant k. The system is located on a horizontal frictionless surface and executes simple harmonic motion. 12. Let M = 8 kg and k = 200 N/m. At time t = 0, the block is at its equilibrium position and has a velocity of 2 m/sec in the *x direction. What is the acceleration of the block at the instant t = 0.50 sec ? a. 8.01 m/sec^2 in the -x direction b. 5.98 m/sec^2 in the -x direction c. 10.00 m/sec^2 in the -x direction d. 5.98 m/sec^2 in the +x direction e. 8.01 m/sec^2 in the +x direction

Explanation / Answer

11)

in SHM

Force is proportional to displacement , and is in opposite direction of displacement

so option is

e) Ma = Fnet = - alpha X

12)

we know that

a = - Aw^2 sin wt

a = -2x w sin wt

a = -2x 5 sin 5t

at t = 0.5sec

substituting we get

a = -5.984 m/s^2 ( - x direction)

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