Questions in Oscillations

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The phase (at a time t) of a particle in simple harmonic motion tells
A particle is moving with constant angular velocity along the circumference of a circle. Which of the following statements is true
A particle is executing simple harmonic motion with a period of T seconds and amplitude a metre. The shortest time it takes to reach a point $\frac{a}{\sqrt{2}}m$ from its mean position in seconds is
A simple harmonic motion is represented by $F(t)=10\sin \,(20\,t+0.5)$. The amplitude of the S.H.M. is
Which of the following equation does not represent a simple harmonic motion
A particle in S.H.M. is described by the displacement function $x(t)=a\cos (\omega t+\theta )$. If the initial $(t=0)$ position of the particle is 1 cm and its initial velocity is $\pi \,cm/s$. The angular frequency of the particle is $\pi \,rad/s$, then it’s amplitude is
A particle executes a simple harmonic motion of time period T. Find the time taken by the particle to go directly from its mean position to half the amplitude
A particle executing simple harmonic motion along y-axis has its motion described by the equation $y=A\sin (\omega \,t)+B$. The amplitude of the simple harmonic motion is
A particle executing S.H.M. of amplitude 4 cm and T = 4 sec. The time taken by it to move from positive extreme position to half the amplitude is
Which one of the following is a simple harmonic motion

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