The velocity of an object in simple harmonic motion is given by v(t)= -(0.275 m/s)sin(23.0t + 2.00π), where t is in seconds.
1) What is the first time after t=0.00 s at which the velocity is -0.100 m/s?
2) What is the object's position at that time?
I tried solving for time and got -13.019 which is wrong :(. It can't even be negative so I don't know what to do.
Remember it is the same at the same time every period.(every 2pi inside the sine function so forget the 2 pi in there.)
Now from t = 0 to 23t = 2 pi is a period so
period T = 2 pi/23 = .273 seconds
v(t)= -(0.275 m/s)sin(23.0t + 2.00π)
-.1 = -(0.275 m/s)sin(23.0t)
sin 23 t = .364
23 t = .372 rad
t = .0162 seconds
Thanks, I see how it's done. For question 2, I did: x = dv/dt = 0.275*cos(23t) = 0.275*cos(0.372rad) = 0.256 m which is incorrect for some reason.
To find the first time after t=0.00 s at which the velocity is -0.100 m/s, you need to set the equation for velocity equal to -0.100 m/s and solve for t.
Given: v(t) = -(0.275 m/s)sin(23.0t + 2.00π)
To solve for t, set v(t) equal to -0.100 m/s:
-0.100 = -(0.275 m/s)sin(23.0t + 2.00π)
Now, divide both sides of the equation by -(0.275 m/s) to isolate the sine term:
sin(23.0t + 2.00π) = -0.100 / -(0.275 m/s)
This simplifies to:
sin(23.0t + 2.00π) = 0.364
To find the first time the sine function has a value of 0.364, you can use the inverse sine function (arcsin or sin^(-1)):
23.0t + 2.00π = arcsin(0.364)
To solve for t, subtract 2.00π from both sides:
23.0t = arcsin(0.364) - 2.00π
Then, divide both sides by 23.0 to isolate t:
t = (arcsin(0.364) - 2.00π) / 23.0
By evaluating this expression using a calculator, you can find the value of t.
Note that t represents time and should be positive. If you obtained a negative value for t, it is likely due to an error in your calculations or a mistake in the order of operations. Double-check your calculations and make sure you are using the correct units and trigonometric functions.