A body moving at simple harmonic motion has an amplitude 50cm and a frequency of 50HZ ,find
(a) the period of oscillation
(b) the acceleration of the maximum displacement
Isn't period the reciprocal of frequency?
y=position- Asin(2PI*f*t)
y'=velocity=A*2pif cos..
y"=accleration=A (2piIf)^2 sin...
T = 1/f = 1/50 seconds
x = 0.50 sin w t where w = 2 pi f
v = 0.50 w cos w t
a = -0.50 w^2 sin wt = -w^2 x
maximum of sin is 1.00
so
a max = -0.50 (4 pi^2* 50^2)
To find the period of oscillation for a body in simple harmonic motion, you can use the formula:
T = 1 / f
Where:
T is the period of oscillation
f is the frequency of the motion
Given that the frequency (f) is 50 Hz, we can plug this value into the formula:
T = 1 / 50
T = 0.02 seconds
So, the period of oscillation is 0.02 seconds.
Now, to find the acceleration at the maximum displacement, you can use the formula:
a = 4π²f²x
Where:
a is the acceleration
f is the frequency
x is the amplitude
Given that the frequency (f) is 50 Hz and the amplitude (x) is 50 cm, we can plug these values into the formula:
a = 4π²(50)²(50)
a = 4π²(2500)(50)
a = 4π²(125000)
a = 50000π²
So, the acceleration at the maximum displacement is 50000π².
To find the period of oscillation of a body in simple harmonic motion, we can use the formula:
T = 1 / f
where T represents the period and f represents the frequency.
(a) The period of oscillation is given by:
T = 1 / f
T = 1 / 50 Hz
T = 0.02 seconds
So, the period of oscillation is 0.02 seconds.
To find the acceleration of the maximum displacement in simple harmonic motion, we can use the formula:
a = -(2πf)^2 * x
where a represents the acceleration, f represents the frequency, and x represents the maximum displacement.
(b) The maximum displacement is given by the amplitude, which is given as 50 cm.
So, the acceleration of the maximum displacement is:
a = -(2πf)^2 * x
a = -(2π * 50 Hz)^2 * 50 cm
a = -(2π * 50 * 2 * 3.14)^2 * 50 cm
a ≈ -196000 cm/s^2
So, the acceleration of the maximum displacement is approximately -196,000 cm/s^2.