A particle on a spring executes simple harmonic motion. If the mass of the particle and the amplitude are both doubled then
(a) the period of oscillation will change by a factor of
(A) 4. (B) ![src=data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACUAAAAuCAIAAAAgO0eXAAAA6klEQVRYhe3V3Q3EIAgAYOdyIOZxGpZxmN6DTeXPU1qvySX42EQ+RLDpeHel8MLb7iGkhbXNQ0iAS4lt8RBSLvU1r5a8jVvwFFdLprfmy2Xqca5Z/cNpr9/uzKslk2gI6kAyg4cea80WWxzGyOG+JybBio3gKWj3EHSaavBU9Xxa8+jrwbbag8f70zkqpJ7qdqzBExV91p88mMEN729Z5P1C9444Gdo3EKI/+2Y+eF9CPznf0Utm/xPO1hIvwJXC3Nbzd7XfaJv4GdLj3vG8FfIt832pJe/74y14P1zhhRdeeOGFF154/+Z9AERsrCH5fbowAAAAAElFTkSuQmCC]()
(C) 2. (D) ![src=data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAkCAIAAAD+cXYAAAAAyklEQVRIie3UyxEEIQgEUOIiIOIhGpIhGPagTjkqI86nag9y92m1rWBfDmx961tPIwSBuakLAcm9Q891IUDWj3RlfIr7eocrY512KDNPP+Ppeg8w3/Z8A0dXxnqxUGM12y3qs7o80md4uoNAMkLQFW+CR22zUQOuiy4UbYwZ9Ce5KroyhmlLuQtBlY6PL9JZPzXAxbtWRvWcDrK2Ra+P3Wwa+SlKI0s647o4X3HR3fYffT++kTi+oIff38rUb3UQ7ov6+7P1rf+X/gN5KPnAlmq33gAAAABJRU5ErkJggg==]()
(b) the maximum speed of the particle will change by a factor of
(A) 4. (B) ![src=data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACYAAAAiCAIAAAC8zjzvAAAA40lEQVRIie2Vyw3EIAxEqYuCXA/VuBmKyR4SBfwBDQuL9oCPSPj5MwPh2h7hIA9yG5IpALESyRSIx4qcRDKFmPJOZE5xAXEEaYg5xXqDaDk4UhJvXDl48MimYWROsUrIZNrSRcwjhVjv9Kolp4wppLKHl54Jm6yDZLLFGkOaMaJAhazfFnHbN6RULOwfb7BmU54divWinFSvzOcTmLgFoQz719RZRZ0dd0lJsuS8N2ck+2eVVZuf/Ho/S1OPwVtHDd3z5CrJVuPo866a/ROKjGov+65NTXPFDjiB/Egd5kAf5f8gPJPnipOaVp00AAAAASUVORK5CYII=]()
(C) 2. (D) ![src=data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADEAAAAlCAIAAABkuZbGAAAA7klEQVRYhe3Wyw2EMAwE0NTlglyPq3EzLmb3AEQhX2fXBoQyZyQeij0hfJ6XcDegkmXS5R0mxqDIpSbGgPzPG8eZNTEGIHGhxEyahMCdNGkqSEKQTpHNqU6ZzqRt2CNjn30D1oxJCNJXMmaCDHmJabRyN5hGpG223M6OMRQrPyCZiUpT2tL5sHRagNFs65pnV3x1r5iEwA7UNu1fHhltkjWoZzptUZNU9IGvaT8/IMmLKX0go5rcPd0uOM6vvnKNn5bD9Htb9fspXmd6krvJrptnMuzxytB45x3/4/5ZJl2WSZdl0mWZdFkmXZ5o+gK2dxg+gWzlRAAAAABJRU5ErkJggg==]()
(c) the magnitude of the maximum acceleration of the particle will change by a factor of\
(A) 4. (B) ![src=data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACYAAAAkCAIAAABql9/yAAAA40lEQVRYhe2VyxEDIQiGrcuCqMdqaMZiNofdUXmYQDTmAkdn4OP1Y7qOWwpkIA8gEZLBdiIREqA1vS1IhJRLPYmsJW8j2pCCWEseJ+hLx4KkxBvXHx68fdIGZC15CIggyuJJrCPJst7hWUlKGktIJg8tPIKnswSJIJMVghRt9AEbcrwtxFsXJN1Yp35oY8WkNEGy1i5vLI2nEKezNEPF+ozuMyKP7lOJ3NjuTwX5JvpilVfvnf57PJvGjkPL4jNe1WVbyJkn+zzHor9Eelvls9n1qSXv+yFtyB9aIAMZyED+B/kCqXPFz/ltfH4AAAAASUVORK5CYII=]()
(C) 2. (D) ![src=data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACcAAAAjCAIAAACYUIR0AAAA0klEQVRYhe3VyxHEIAgGYOqyIOqhGpqxmN1DjGNAIz6SXOC8sx+D/AR+XxS4qosRDLVZZQRka4e7VEYIFF9WI4WdqE1VaKRQvubw7C3qFT3WKkNpy8ZggxoplH/KKAzRxia1t76PqD30eOOFCTOCCkgHnTGzWl4e+Wg3mWGc2WA5YdX5XVAjhSlSqan7DLXRBbKiXjayiar0rKppyoGiDGr5A9HM6MWsJeeccn19G5+8UzWlt5rXfGbt6AZ16t6MVOs2VR7vBfXZctVVV1119Vv1D+un3SRVFOyqAAAAAElFTkSuQmCC]()
(E) 1 (it remains unchanged).