A particle of mass m=1kg is attached to a spring. Its motion is described by the

Question

A particle of mass m=1kg is attached to a spring. Its motion is described by the following equation:

(d^2x/dt^2)+(9/sec^2)x=0,,,,, sec^2 is second  squared.

Where x is the position of the mass measured from the equillibirium position. The units of x is in meters and the units of t in seconds.

A) calculate the angular frequecy (rad/sec) and the period of the oscillations.

B) Indicate, based only on the information given above, whether or not it is possible to determine:-

i) The amplitude of the oscillations, and

ii) The value of the spring-constant

If you answer were affirmative, provide the corresponding value.

C) the following additional information is provided: when the mass m passes through the equillibirium position, its velocity is 1m/s. Indicate whether or not it is possible to determine:

i) the amplutide of the oscillations and

ii) The value of the spring-constant

If you answer were affirmative, Provide the corresponding value.

Explanation / Answer

angular frequency be omwga

then

A. (omega)^2=9 gives omega=3 rad/s

B

i) no amplitude cannot be determined

ii) omega=sqrt[k/m] thus k=9N/m

C)i) yes possible to determine: velocity at eqillibrium position= amplitude*omega^2 thus amplitude=1/9=.11 m

ii) same as in part B K= 9N/m

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