What is the dimension of c3 in s=cs cos(c4t)

Thread starter dovec
Start date Jan 22, 2010
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Dimension

In summary, "dimension" in this equation refers to the unit of measurement used for the variable c3. The dimension of c3 can be determined by examining the units of measurement for each variable, and in this case, it is meters (m). C3 is a constant term in this equation that represents the initial displacement of an object in simple harmonic motion. Its value affects the amplitude and period of the oscillation, with larger values resulting in greater amplitude and longer periods. C3 can have a negative value, but its magnitude still determines the amplitude and the period remains the same.

Jan 22, 2010

dovec

Find the dimension for the quantity c3 in the expression s=c3 cos (c4t). Please someone help me solve this, s is a distance with unit L, t is a time with unit T and theta is an angle in radians.

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Jan 22, 2010

Stonebridge

The dimensions must be the same on both sides of a valid equation.
Left side you just have [L] Length.
Right side: cos(anything) is dimensionless, leaving just c3.

Jan 23, 2010

dovec

Thanks

1. What is the meaning of "dimension" in this equation?

In this equation, "dimension" refers to the unit of measurement used for the variable c3. It is important to note that in physics, the term "dimension" can also refer to the concept of space and time.

2. How do you determine the dimension of c3 in this equation?

The dimension of c3 in this equation can be determined by examining the units of measurement for each variable. In this case, the unit for c3 must be the same as the unit for s, which is meters (m). Therefore, the dimension of c3 is also meters (m).

3. What is the significance of c3 in this equation?

C3 is a constant term in this equation that represents the initial displacement of an object in simple harmonic motion. It is the distance from the equilibrium point at t=0.

4. How does c3 affect the equation and its solutions?

The value of c3 affects the amplitude of the oscillation in this equation. The larger the value of c3, the larger the amplitude of the oscillation. This means that the object will travel a greater distance from the equilibrium point before turning back in the opposite direction. Additionally, the value of c3 also affects the period of the oscillation, with larger values resulting in longer periods.

5. Can c3 have a negative value in this equation?

Yes, c3 can have a negative value in this equation. This would indicate that the object is starting from a position below the equilibrium point at t=0 and would result in a different direction of motion compared to a positive value of c3. However, the magnitude (absolute value) of c3 would still determine the amplitude of the oscillation and the period would remain the same.