Simple Harmonic Physics Questions?

Question

1. The equation of motion of a simple harmonic oscillator is d^2 x/d t^2= -9x, where x is displacement and t is time. The period of oscillation is...?

2.A pendelum with a period of 1 s on Earth, where the accelaration due to gravity is g, is taken to another planet, where its period is 2s. The accelaration due to gravity on the other planet is most nearly...?
A) g/4
B)g/2
C) g
D) 2g
E)4g

Answer 1

1. d^2 x/d t^2= -9x,
x=sin(wt)
w=sqrt (9)=3 rad/sec
T=1/f=2 pi/w= 2 x 3.14159.../ 3=
T=2.1 sec

2. T=2pi sqrt(L/g)
L- length of the pendulum
T1=2pi sqrt(L/g1)

L= (T1/2 pi)^2 g1

T2=2pi sqrt((T1/2 pi)^2 g1/g2)
T2= 2 pi (T1/2 pi) sqrt(g1/g2)

T2/T1=sqrt(g1/g2)
g2=(T1/T2 )^2 g1
g2=(1/2)^2 g1
g2= g1/4

(A) g/4

Answer 2

the final equation of straightforward harmonic action is given as x(t)= A Cos (wt + phi ) it ought to also be Sin, an similar thoughts word to that to boot. comparing the given equation with the final equation you'll have. A= 2 cm ( Amplitude) w=10 => 2 * Pi / T = 10 accordingly T = 2 * Pi / 10 seconds For more effective solutions you are able to attempt out the link decrease than