Finding Mass in SHM with Known Spring Constant and Velocity

In summary, a block with unknown mass attached to a spring with a spring constant of 9.00 N/m undergoes simple harmonic motion with an amplitude of 10.0 cm. When the mass is halfway between its equilibrium position and its maximum positive displacement, its velocity is +30.0 cm/s. Using the formula for velocity as a function of time and the relation between ω and mass, the mass of the block can be calculated to be 0.75 kg.
  • #1
JoulesVerms
1
0

Homework Statement



A block of unknown mass is attached to a spring with a spring constant 9.00 N/m and
undergoes simple harmonic motion, along the x axis, with an amplitude of 10.0 cm. When the
mass is halfway between its equilibrium position and its maximum positive displacement, its
velocity is measured to be +30.0 cm/s. Calculate
(a) the mass of the block,

Homework Equations



??

The Attempt at a Solution



I tried using the x= A cos (ωt +∅) but i can't figure it out without time. HELP?? I know the answer is suposed to be m= 0.750kg but i don't understand how to get there.
 
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  • #2
What is cos(ωt +∅) when the mass is halfway between its equilibrium position and its maximum positive displacement?

What is the formula for velocity as function of t?
How is ω related to mass?

ehild
 
  • #3
Since OP not interested, i find the problem interesting since i just started on SHM.

Using circular motion method.
Since position is halfway between its equilibrium position and its maximum positive displacement,
θ=60°
VmaxCos(90-θ)=0.3 m/s
Vmax=0.3x 2/√3

F=mv2/r
m=0.9 x 0.1 x 3/(0.36)
m=0.75 kg
 

FAQ: Finding Mass in SHM with Known Spring Constant and Velocity

What is the definition of phase constant in SHM?

The phase constant in SHM (Simple Harmonic Motion) is a measure of the initial position of the oscillating object at the starting point of the motion. It is denoted by the symbol phi (φ) and is measured in radians.

How is the phase constant related to the amplitude and period of SHM?

The phase constant is directly related to the amplitude and period of SHM. It determines the starting point of the oscillation and does not affect the amplitude or period of the motion.

How can the phase constant be determined experimentally?

The phase constant can be determined experimentally by measuring the displacement of the oscillating object at different points in time and then using this data to plot a graph. The phase constant can be found by finding the angle between the initial position and the point where the graph crosses the x-axis.

What is the physical significance of the phase constant?

The phase constant represents the initial conditions of the SHM system. It describes the starting position of the oscillating object and can provide information about the energy and direction of the motion.

How does the phase constant affect the motion of an object in SHM?

The phase constant does not affect the motion of the object in SHM. It only determines the starting position of the motion. The amplitude and period of the motion are determined by the initial conditions of the system and the properties of the object, such as its mass and spring constant.

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